A282930 Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.

1, 49, 1274, 23275, 334425, 4015011, 41818315, 387605443, 3256150548, 25135003348, 180196297050, 1210028211210, 7663549175191, 46039891115155, 263630633610437, 1444741006154614, 7604013727493190, 38554851707435000, 188824087108333495, 895363849845490543, 4119191297378031000, 18420594133878904635, 80204828814019528689

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))^48/(1 - x^j)^49: j in [1..30]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^48/(1 - x^k)^49, {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))^48/(1 - x^j)^49)) \\ G. C. Greubel, Nov 18 2018

Sage

R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^48/(1 - x^j)^49 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^48/(1 - x^n)^49.

a(n) ~ exp(Pi*sqrt(590*n/21)) * sqrt(295) / (4*sqrt(3) * 7^(49/2) * n). - Vaclav Kotesovec, Nov 10 2017