A347916 - OEIS

%I #9 Sep 19 2021 08:03:29

%S 1,1,0,6,6,75,1025,1225,43988,471345,5084387,40870181,866782774,

%T 8473297261,165871287465,3934845305287,23390789927784,956832091069057,

%U 21869141108144439,269518811758178785,8437830353620298346,220696789738463945981,3231280243441039496181,125072102239522472394691

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

%F E.g.f.: exp( exp(-x) * Sum_{k>=1} A000593(k)*x^k/k ).

%F E.g.f.: exp( exp(-x) * Sum_{k>=1} x^k/(k*(1 - x^(2*k))) ).

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

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(exp(-x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(exp(-x)*sum(k=1, N, x^k/(k*(1-x^(2*k)))))))

%Y Cf. A000593, A088311, A346548, A347915.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 18 2021