A282931 Expansion of Product_{k>=1} (1 - x^(7*k))^52/(1 - x^k)^53 in powers of x.

1, 53, 1484, 29097, 447426, 5734918, 63638001, 627260142, 5594403499, 45779730871, 347453597091, 2466970932027, 16501339314082, 104588498225862, 631215364345159, 3642533720923593, 20170341090888205, 107511123136305075, 553099301324196585

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))^52/(1 - x^j)^53: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^52/(1 - x^k)^53, {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))^52/(1 - x^j)^53)) \\ G. C. Greubel, Nov 18 2018

Sage

R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^52/(1 - x^j)^53 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^52/(1 - x^n)^53.

a(n) ~ exp(Pi*sqrt(638*n/21)) * sqrt(319) / (4*sqrt(3) * 7^(53/2) * n). - Vaclav Kotesovec, Nov 10 2017