A295792 Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/k).

1, 2, 6, 28, 152, 1008, 7936, 70208, 689664, 7618816, 92013824, 1202362368, 17053410304, 258928934912, 4197838491648, 72840915607552, 1334630802489344, 25799982480556032, 527187369241870336, 11292834065764450304, 253498950169144590336, 5965951790211865772032, 146341359815078034538496

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2017

Keywords

• nonn

Comments

Convolution of A028342 and A168243. - Vaclav Kotesovec, Sep 07 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A001227, A028342, A028343, A054844, A156616, A168243, A206303, A294356.

Programs

Maple

a:=series(mul(((1+x^k)/(1-x^k))^(1/k),k=1..100),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 22; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: exp(2*Sum_{k>=1} A001227(k)*x^k/k).

E.g.f.: exp(Sum_{k>=1} A054844(k)*x^k/k).