A330539 Expansion of e.g.f. Product_{k>=1} (1 + arcsin(x^k)).

1, 1, 2, 13, 48, 389, 3120, 27483, 258384, 3209481, 40895280, 532286415, 8095233960, 125622532125, 2196944928360, 40755258858195, 773235510112800, 15597078326535825, 345588497493916320, 7674105262451228055, 183908428603335286200

Offset: 0

Author

Ilya Gutkovskiy, Dec 17 2019

Keywords

• nonn

Crossrefs

Cf. A001818, A270662, A330540.

Programs

Mathematica

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