It’s bound to be the most interesting class of the fall at New York University, and the one most begging for a punchline — “The Teachable Art of Governing” . . . with David Paterson.

New York’s accidental governor took a lot of hits during a three-year term, which fluctuated from the serious (a budget crisis), the dramatic (vetoing spending measure after spending measure in one all-day session) to the absurd (too many to count, but let’s start with his first press conference, in which he admitted to everything from extramarital affairs to drug use).

Yet no one knows better the trials of trying to survive the dysfunction of Albany. And perhaps, with the success of Gov. Cuomo working off of Paterson’s final stands, there’s a bit of rehabilitation on the table, a rethinking of his legacy?

“Some of the decisions I made certainly laid the foundation, certainly set the tone, that I wouldn’t be able to run again,” Paterson says, “but I think the new governor’s success and approach by continuing some of these policies validates them.”

That includes the elimination of “pork barrel” spending and balancing the budget with no borrowing — though he did have to increase some taxes.

“When Cuomo came in, he did exactly the same thing,” Paterson says. “He balanced a $10 billion deficit. He didn’t have to tax in that situation, but when you have $21 billion you will have to tax, I assure you.”

Just eight months after Paterson left office, political scientist Fred Siegal thinks a re-evaluation of the successes of his term is warranted. Though green at the start, he said, Paterson made decisions that restored power to the office, which had been diminished by Pataki’s weakness and Spitzer’s collapse.

But, Siegal says, his image slid downhill after he tapped Kirsten Gillibrand to replace Hillary Clinton in the Senate after an embarrassing leak from his office derailed Caroline Kennedy’s chance at the seat.

“It was hard for him to overcome the sense that he was in over his head,” Siegal says.Nevertheless, Paterson learned from his “dramatic” years heading the state in the wake of Spitzer’s prostitution scandal.

Thrust into office in 2008, he immediately left the public rollicking by dusting off his own skeletons: dalliances outside of his marriage and cocaine use. “A poll said 82% could care less about my marital issues and 90% could care less that I tried drugs,” he laughs, “because 90% of them did.”

But airing dirty laundry just provided ammunition to political enemies down the road, he says.

Coupled with his blindness — which was lampooned by “Saturday Night Live” and used by critics in Albany — those foes were very well armed.

“I was depicted as someone who bumped into walls, which I don’t recall ever doing that. I don’t have any pictures of me with welts on my eye from banging into walls,” he says. It was “kind of like that cartoon character Mr. Magoo that blind equals stupid and bumbling and fumbling and that kind of thing.”

“It was the only thing that they found interesting about me,” he says of “SNL,” “other than that I didn’t like New Jersey.”

A legislator even predicted disaster when his secretary resigned because she read to him. “There’s no one in the state who could read?” he asks incredulously.

While being mocked, he carried on with state business, he says, but there were bumps until the end. Someone in his office divulged Kennedy’s tax issues when she was a front-runner for the Senate seat. Paterson, charged with making that appointment, says that afterwards, “Everybody in the office was pointing fingers at each other.”

Then came the infamous coup led by disgraced state Senators Pedro Espada and Hiram Monserrate. One silver lining: He helped clear up whether a governor could appoint a lieutenant governor. It turned out he could.

“If I took Spitzer’s place again, then I could appoint a lieutenant governor and then I could have appointed myself to the US Senate,” he jokes.

But by February 2010, everything crumbled when a damning New York Times article revealed that his top aide sexually assaulted his girlfriend, and that the governor personally had conversations with his victim afterwards. Less than a week after publication, he abandoned his bid for re-election.

Even after all that, he faced the embarrassment of the Yankee ticket debacle, which lead to a $60,000 ethics commission fine, a decision Paterson still finds puzzling. “Is there anybody in the state aside from good government-groups that thinks the governor should not go to the World Series?” he says.

Of course, he has regrets.

“I made the mistake of living crisis to crisis. What I should have done was to pass the budget, stop the train and re-evaluate all the people who were with me,” he says. “Also I had a tendency to use the McDonald’s theory [that] if someone leaves, just promote from within.”

“If you want to change an institution, you’ve got to take it apart like the governor’s doing now,” he says. “He’s merging agencies. He’s getting rid of people who have been sitting there inactive in the last 100 years.

“It was challenging and difficult,” he says of his time in office, “and I don’t think that I recognized for a couple of months how rewarding it was.”

Now in his political afterlife, he’s teaching, consulting and doing occasional radio gigs on WFAN and WOR. “I’m hoping that that will one day develop into a regular position,” Paterson says. The class kicks off in early September, and he’s cramming the course material, tape-recorded for him by NYU and an intern. “If you could face the the national media you should be able to answer the questions of 20 to 30 college freshman,” he says.

Paterson also gets to play political prognosticator, as with the 2013 race for mayor. Bill Thompson, in his eyes, is the current frontrunner and likely winner. But he didn’t discount others mulling a run, like Police Commissioner Ray Kelly. “Every place I go I see Kelly,” he laughs. “I going in the shower the other day and I saw Ray Kelly.”

Paterson, so far, has no plans of his own to get back into politics, but didn’t eliminate the possibility.

“A lot of people do it because they want to clear something up or settle scores or have a grand political comeback, but I’m not interested in political appearance at this point,” he says. “If it were something that I thought was rewarding then I would think about it.

“Sometimes you see some people in politics and they remind you of old boxers because they’re almost punchy,” he laughs. “They got hit so much they can’t even speak anymore and I think too many people in politics don’t know when to get out.”