A278557 Expansion of Product_{n>=1} (1 - x^(5*n))^24/(1 - x^n)^25 in powers of x.

1, 25, 350, 3575, 29575, 209381, 1312075, 7443825, 38854075, 188836375, 862496902, 3729343275, 15356254650, 60511763600, 229125615600, 836555203223, 2953900713000, 10113407774450, 33649438734125, 109017926343725, 344525085375315, 1063718962906450

Offset: 0

Author

Seiichi Manyama, Nov 23 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A160460, A278555, A278556, A278558, A278559.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^24/(1 - x^k)^25, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 28 2016 *)

Formula

G.f.: Product_{n>=1} (1 - x^(5*n))^24/(1 - x^n)^25.

A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*A278556(n-2) + 5^10*6*a(n-3) + 5^12*A278558(n-4) for n >= 4.

a(n) ~ sqrt(101/15) * exp(Pi*sqrt(202*n/15)) / (976562500*n). - Vaclav Kotesovec, Nov 28 2016