A335635 Expansion of e.g.f. Product_{k>0} 1/(1 - sin(x)^k / k).

1, 1, 3, 10, 44, 215, 1252, 7992, 56024, 438341, 3672328, 32587366, 318586880, 3325053147, 35115462592, 407034567076, 5198294627456, 63965057355305, 824995119961984, 12611299833296898, 184189806819806720, 2590874864719588031, 44912343151409875456, 728583107189913021328, 11458864344772729650176

Offset: 0

Author

Seiichi Manyama, Oct 03 2020

Keywords

• sign

Comments

a(30) is negative.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A007841, A335626, A335636, A335637, A335642.

Programs

Mathematica

max = 24; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Sin[x]^k/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 03 2020 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-sin(x)^k/k)))

PARI

N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, sin(x)^(i*j)/(i*j^i))))))

Formula

E.g.f.: exp( Sum_{i>0} Sum_{j>0} sin(x)^(i*j)/(i*j^i) ).