A330543 Expansion of e.g.f. Product_{k>=1} (1 + arctan(x^k)).

1, 1, 2, 10, 48, 344, 2400, 22128, 223104, 2520576, 30689280, 415560960, 6058229760, 95710187520, 1602520657920, 28908021381120, 554882885222400, 11182172398387200, 237581975468113920, 5324332409912033280, 125630406117045043200

Offset: 0

Author

Ilya Gutkovskiy, Dec 17 2019

Keywords

• nonn

Crossrefs

Cf. A010050, A270666, A330544.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + ArcTan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcTan[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arctan(x^(k/d))^d / d).