A335626 Expansion of e.g.f. Product_{k>0} 1/(1-sin(x)^k).

1, 1, 4, 17, 104, 661, 5584, 47837, 483584, 5332681, 63940864, 802442057, 11548580864, 170258934301, 2602357970944, 44379608478677, 800966933970944, 14221966162901521, 277738909303373824, 5823354583392253697, 121050262784565837824, 2668717158207399650341, 62376912442894992277504

Offset

0,3

Comments

a(46) is negative. - Vaclav Kotesovec, Oct 03 2020

Links

Seiichi Manyama, Table of n, a(n) for n = 0..400 (terms n = 0..100 from Vaclav Kotesovec)

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000041, A335627, A335629.

Sequence in context: A091635 A306160 A127676 * A232211 A122940 A077386

Adjacent sequences: A335623 A335624 A335625 * A335627 A335628 A335629

Keyword

sign

Author

Seiichi Manyama, Oct 02 2020

Status

approved