A278556 Expansion of Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19 in powers of x.

1, 19, 209, 1710, 11495, 66862, 347339, 1645875, 7221520, 29668595, 115116233, 424720338, 1498263563, 5076482415, 16583497160, 52399330389, 160586833362, 478482249548, 1388989067820, 3935549005725, 10901608510397, 29565343541110, 78604103339462

Offset: 0

Author

Seiichi Manyama, Nov 23 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. Product_{n>=1} (1 - x^(5*n))^k/(1 - x^n)^(k + 1): A160461 (k=1), A160462 (k=2), A160463 (k=3), A160506 (k=4), A071734 (k=5), A160460 (k=6), A160521 (k=7), A278555 (k=12), this sequence (k=18), A278557 (k=24), A278558 (k=30).

Programs

Mathematica

CoefficientList[ Series[ Product[(1 - x^(5n))^18/(1 - x^n)^19, {n, 22}], {x, 0, 22}], x] (* Robert G. Wilson v, Nov 24 2016 *)

Formula

G.f.: Product_{n>=1} (1 - x^(5*n))^18/(1 - x^n)^19.

A278559(n) = 5^2*63*A160460(n) + 5^5*52*A278555(n-1) + 5^7*63*a(n-2) + 5^10*6*A278557(n-3) + 5^12*A278558(n-4) for n >= 4.

a(n) ~ sqrt(77/15) * exp(Pi*sqrt(154*n/15)) / (7812500*n). - Vaclav Kotesovec, Nov 28 2016