%I #30 Sep 18 2021 07:57:07
%S 1,0,2,9,40,360,2480,28833,266936,3562920,45634258,659631225,
%T 10231705196,176661237948,3080315922294,59430009554685,
%U 1217593208993232,25766943601055184,583245289316927058,13861911731632256457,343615639889119016556,8925102256331257339140,242399591002192962709230
%N E.g.f.: Product_{k>=1} 1 / (1 - x^k)^sin(x).
%F E.g.f.: exp( sin(x) * Sum_{k>=1} sigma(k)*x^k/k ).
%F E.g.f.: exp( sin(x) * Sum_{k>=1} x^k/(k*(1 - x^k)) ).
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^sin(x))))
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sin(x)*sum(k=1, N, sigma(k)*x^k/k))))
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sin(x)*sum(k=1, N, x^k/(k*(1-x^k))))))
%Y Cf. A000203, A053529, A335626, A346547, A346941, A347774.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 18 2021