A347916 E.g.f.: Product_{k>=1} (1 + x^k)^exp(-x).

1, 1, 0, 6, 6, 75, 1025, 1225, 43988, 471345, 5084387, 40870181, 866782774, 8473297261, 165871287465, 3934845305287, 23390789927784, 956832091069057, 21869141108144439, 269518811758178785, 8437830353620298346, 220696789738463945981, 3231280243441039496181, 125072102239522472394691

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

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

Prog

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

Crossrefs

Cf. A000593, A088311, A346548, A347915.

Sequence in context: A269767 A065239 A146892 * A361738 A320824 A085804

Adjacent sequences: A347913 A347914 A347915 * A347917 A347918 A347919

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2021

Status

approved