A330537 Expansion of e.g.f. Product_{k>=1} 1 / (1 - arctan(x^k)).

1, 1, 4, 16, 104, 704, 6368, 58752, 662272, 7802880, 106639872, 1511241216, 24062834688, 398765162496, 7252942872576, 137324083666944, 2804224273514496, 59594575901687808, 1352293406316822528, 31831016595468189696

Offset: 0

Author

Ilya Gutkovskiy, Dec 17 2019

Keywords

• nonn

Crossrefs

Cf. A010050, A270665, A330538.

Programs

Mathematica

nmax = 19; CoefficientList[Series[Product[1/(1 - ArcTan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[Exp[Sum[Sum[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} arctan(x^(k/d))^d / d).