A282925 Expansion of Product_{k>=1} (1 - x^(7*k))^28/(1 - x^k)^29 in powers of x.

1, 29, 464, 5365, 49880, 394632, 2750969, 17296732, 99742368, 534126988, 2681856693, 12722233068, 57373155952, 247218913828, 1022189562610, 4070289420139, 15656921120982, 58336024110584, 211023516790156, 742643172981206, 2547265600634862, 8529351700138885

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))^28/(1 - x^j)^29: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^28/(1 - x^k)^29, {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))^28/(1 - x^j)^29)) \\ G. C. Greubel, Nov 18 2018

Sage

R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^28/(1 - x^j)^29 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^28/(1 - x^n)^29.

a(n) ~ exp(Pi*sqrt(350*n/21)) * sqrt(175) / (4*sqrt(3) * 7^(29/2) * n). - Vaclav Kotesovec, Nov 10 2017