A282921 Expansion of Product_{k>=1} (1 - x^(7*k))^12/(1 - x^k)^13 in powers of x.

1, 13, 104, 637, 3276, 14820, 60697, 229360, 810498, 2705118, 8592857, 26134654, 76476816, 216174700, 592220696, 1576826355, 4090222409, 10357895639, 25653139694, 62235901689, 148108568986, 346176981673, 795569268689, 1799508071426, 4009753651904, 8808973137510

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))^12/(1 - x^j)^13: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^12/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

PARI

my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^12/(1 - x^j)^13)) \\ G. C. Greubel, Nov 18 2018

Sage

m = 30
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(m)
s = prod((1 - x^(7*j))^12/(1 - x^j)^13 for j in (1..m))
list(s) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^12/(1 - x^n)^13.

a(n) ~ exp(Pi*sqrt(158*n/21)) * sqrt(79) / (4*sqrt(3) * 7^(13/2) * n). - Vaclav Kotesovec, Nov 10 2017