A335629 Expansion of e.g.f. Product_{k>0} (1+sin(x)^k).

1, 1, 2, 11, 40, 241, 1952, 13691, 96640, 1124161, 13770752, 119165771, 1373271040, 21966388081, 297353879552, 4935774720251, 71240808202240, 589721910720001, 20308058536804352, 594276723452229131, 4142005120030474240, 73558191271194967921, 5026768573876078641152, 36395755978909448444411, -115943295497314720808960

Offset: 0

Author

Seiichi Manyama, Oct 02 2020

Keywords

• sign

Links

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

Crossrefs

Cf. A000009, A335626, A335630.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Product[1 + Sin[x]^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 03 2020 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(eta(sin(x)^2)/eta(sin(x))))

PARI

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

PARI

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

Formula

E.g.f.: exp( Sum_{k>0} (-sin(x))^k/(k*(sin(x)^k-1)) ).

Extensions

Two more terms from Vaclav Kotesovec, Oct 03 2020