NEW YORK — Phish announced its 13-show run in New York with a video in January that showed giant doughnuts rolling through the city.

That got Felicia D’Ambrosio’s phone buzzing, with calls from friends hoping that might mean a role for the Phish superfan and co-owner of a Philadelphia doughnut and fried chicken shop that had made doughnuts dedicated to the band in the past.

“Well, no, I don’t want to work on Phish tour,” thought D’Ambrosio, who has been to more than 100 shows.

Then came the request. From the band.

Time to make the doughnuts.

Doughnuts are everywhere in Phish’s “Baker’s Dozen” residency at Madison Square Garden, which kicked off last week and lasts until Aug. 6, from the tickets to a huge mural to the thousands of Federal Donuts being given out to fans each night. The band is even working each night’s custom flavor into its setlists.

The band “never stops surprising me and delighting me and I trust them,” D’Ambrosio said. “To us at Federal Donuts, it’s this weird collaboration of this thing you love and this thing you love.”

Phish’s doesn’t need gimmicks to draw fans to their mostly sold-out shows, but they are known for playful gags on stage. One song features guitarist Trey Anastasio and bass player Mike Gordon performing while jumping on trampolines, and drummer Jon Fishman’s other instruments include a vacuum cleaner.

It was Fishman’s standard outfit – a blue dress covered with red doughnut shapes – that first inspired D’Ambrosio to whip up The Fishman – a blue vanilla raspberry doughnut with a pink glaze – ahead of a 2015 show.

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