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

Author

Seiichi Manyama, Feb 24 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A282919.

Programs

Magma

m:=30; R:=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

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 *)

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

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