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

0,2

Links

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

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

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 *)

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).

Sequence in context: A180364 A125407 A289423 * A023017 A022647 A032613

Adjacent sequences: A278553 A278554 A278555 * A278557 A278558 A278559

Keyword

nonn

Author

Seiichi Manyama, Nov 23 2016

Status

approved