A282926 Expansion of Product_{k>=1} (1 - x^(7*k))^32/(1 - x^k)^33 in powers of x.

1, 33, 594, 7667, 79101, 691119, 5299019, 36518791, 230122266, 1343028082, 7331536586, 37731144564, 184232285897, 857974579385, 3827695162667, 16420097827188, 67948512704413, 271990545250303, 1055719283332541, 3981884465793740, 14621550982740229

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))^32/(1 - x^j)^33: j in [1..m]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^32/(1 - x^k)^33, {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))^32/(1 - x^j)^33)) \\ G. C. Greubel, Nov 18 2018

Sage

R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^32/(1 - x^j)^33 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^32/(1 - x^n)^33.

a(n) ~ exp(Pi*sqrt(398*n/21)) * sqrt(199) / (4*sqrt(3) * 7^(33/2) * n). - Vaclav Kotesovec, Nov 10 2017