A330534 Expansion of e.g.f. Product_{k>=1} 1 / (1 - arcsin(x^k)).

1, 1, 4, 19, 128, 929, 9008, 88677, 1068496, 13585713, 195465552, 2962147101, 50411419368, 887757722409, 17125724016984, 346462040798229, 7503508038803616, 169554609033560673, 4085808543521351136, 102156453049201047981

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Mathematica

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

Crossrefs

Cf. A001818, A330514, A330535.

Sequence in context: A192944 A306179 A330515 * A366182 A330494 A352306

Adjacent sequences: A330531 A330532 A330533 * A330535 A330536 A330537

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 17 2019

Status

approved