A282928 Expansion of Product_{k>=1} (1 - x^(7*k))^40/(1 - x^k)^41 in powers of x.

1, 41, 902, 14063, 173635, 1801745, 16300739, 131814181, 969824701, 6579564585, 41587633402, 246925024493, 1386436741480, 7402293438974, 37755020009290, 184685764132377, 869379223328495, 3949788012868677, 17363552010806127

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^40/(1 - x^n)^41.

a(n) ~ exp(Pi*sqrt(494*n/21)) * sqrt(247) / (4*sqrt(3) * 7^(41/2) * n). - Vaclav Kotesovec, Nov 10 2017

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^40/(1 - x^k)^41, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Prog

(PARI) my(m=30, x='x+O('x^m)); Vec(prod(j=1, m, (1 - x^(7*j))^40/(1 - x^j)^41)) \\ G. C. Greubel, Nov 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^40/(1 - x^j)^41: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018

Crossrefs

Cf. A282919.

Sequence in context: A364994 A182359 A090836 * A114529 A300173 A293619

Adjacent sequences: A282925 A282926 A282927 * A282929 A282930 A282931

Keyword

nonn

Author

Seiichi Manyama, Feb 24 2017

Status

approved