A335635 - OEIS

A335635

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

%I #23 Oct 04 2020 08:46:57

%S 1,1,3,10,44,215,1252,7992,56024,438341,3672328,32587366,318586880,

%T 3325053147,35115462592,407034567076,5198294627456,63965057355305,

%U 824995119961984,12611299833296898,184189806819806720,2590874864719588031,44912343151409875456,728583107189913021328,11458864344772729650176

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

%C a(30) is negative.

%H Seiichi Manyama, <a href="/A335635/b335635.txt">Table of n, a(n) for n = 0..400</a>

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

%t max = 24; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Sin[x]^k/k), {k, 1, max}], {x, 0, max}], x] (* _Amiram Eldar_, Oct 03 2020 *)

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-sin(x)^k/k)))

%o (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))))))

%Y Cf. A007841, A335626, A335636, A335637, A335642.

%K sign

%O 0,3

%A _Seiichi Manyama_, Oct 03 2020