%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