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A335626
Expansion of e.g.f. Product_{k>0} 1/(1-sin(x)^k).
6
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 02 2020
STATUS
approved