A347817 - OEIS

%I #82 Sep 19 2021 11:30:41

%S 1,0,2,3,40,80,1760,8211,139256,763272,19466578,147696835,3372858476,

%T 33370016316,872184749046,10340382875655,289042962136272,

%U 3884706041971728,118640349946950738,1911641854423398435,59577007012206421356,1086774235381609797540,37138839666110194130670

%N E.g.f.: Product_{k>=1} (1 + x^k)^sin(x).

%F E.g.f.: exp( sin(x) * Sum_{k>=1} x^k / (k*(1 - x^(2*k))) ). - _Ilya Gutkovskiy_, Sep 18 2021

%F E.g.f.: exp( sin(x) * Sum_{k>=1} A000593(k)*x^k/k ). - _Seiichi Manyama_, Sep 18 2021

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(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>>valuation(k, 2))*x^k/k))))

%Y Cf. A000593, A088311, A265024, A335629, A346841, A347893, A347894, A347898.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 18 2021