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

0,2

Links

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

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

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 *)

Crossrefs

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

Sequence in context: A119785 A067457 A055333 * A282924 A022653 A125460

Adjacent sequences: A278554 A278555 A278556 * A278558 A278559 A278560

Keyword

nonn

Author

Seiichi Manyama, Nov 23 2016

Status

approved