A335637 Expansion of e.g.f. Product_{k>0} (1 + sin(x)^k / k).

1, 1, 1, 4, 10, 25, 210, 978, 2336, 25265, 361424, 1557752, -1098528, 140915385, 2093367328, 10484632486, 133131785728, -1343478380255, -8738565516288, 1790935681747980, 3245598828836864, -592809746388403495, 6832010190766985216, 179327221659613996634, -5310378915096702812160

Offset: 0

Author

Seiichi Manyama, Oct 03 2020

Keywords

• sign

Crossrefs

Cf. A007838, A335629, A335635, A335638, A335644.

Programs

Mathematica

max = 24; Range[0, max]! * CoefficientList[Series[Product[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(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, (-1)^(i+1)*sin(x)^(i*j)/(i*j^i))))))

Formula

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