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A335642
Expansion of e.g.f. Product_{k>0} 1/(1 - sin(x)^k / k!).
3
1, 1, 3, 9, 35, 147, 710, 3780, 21391, 136063, 932190, 6887232, 55902274, 497726270, 4711586833, 47692742905, 528539419087, 6093676850975, 73010887114406, 943925266298096, 12740929019736310, 175037826035276730, 2561985529052306447, 39817440376814520907, 622315443336146270858
OFFSET
0,3
COMMENTS
a(74) is negative. - Vaclav Kotesovec, Oct 04 2020
FORMULA
E.g.f.: exp( Sum_{i>0} Sum_{j>0} sin(x)^(i*j)/(i*(j!)^i) ).
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 04 2020 *)
PROG
(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))))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 03 2020
STATUS
approved