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%I #18 Sep 19 2021 11:31:56
%S 1,1,2,9,30,195,1545,12474,95564,1199397,14287845,167518846,
%T 2341450386,34489552331,540927170147,10114629115798,175935142966408,
%U 3184271322683385,68623817313870153,1442553498798565142,31856896467060026670,787164874800260366287,19097783293834170329239
%N E.g.f.: Product_{k>=1} (1 + x^k)^cos(x).
%F E.g.f.: exp( cos(x) * Sum_{k>=1} x^k / (k*(1 - x^(2*k))) ). - _Ilya Gutkovskiy_, Sep 18 2021
%F E.g.f.: exp( cos(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)^cos(x))))
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(cos(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))
%Y Cf. A000593, A265024, A346941, A347817, A347894, A347899.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 18 2021
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