A282924 Expansion of Product_{k>=1} (1 - x^(7*k))^24/(1 - x^k)^25 in powers of x.

1, 25, 350, 3575, 29575, 209405, 1312675, 7452201, 38939275, 189537775, 867436570, 3760131375, 15529994130, 61413915500, 233488417752, 856388420815, 3039281123900, 10463551169370, 35024068485525, 114205431037285, 363408170015065, 1130218949978428, 3440267279234290, 10261830946893750, 30029624283800440, 86300123835692431

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))^24/(1 - x^j)^25: j in [1..m+2]]) )); // G. C. Greubel, Nov 18 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^24/(1 - x^k)^25, {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))^24/(1 - x^j)^25)) \\ G. C. Greubel, Nov 18 2018

Sage

R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^24/(1 - x^j)^25 for j in (1..prec))
print(s.coefficients()) # G. C. Greubel, Nov 18 2018

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^24/(1 - x^n)^25.

a(n) ~ exp(Pi*sqrt(302*n/21)) * sqrt(151) / (4*sqrt(3) * 7^(25/2) * n). - Vaclav Kotesovec, Nov 10 2017