A284629 Expansion of (eta(q)eta(q^10)/(eta(q^2)eta(q^5)))^6 in powers of q.

1, -6, 15, -26, 51, -96, 136, -186, 297, -422, 537, -792, 1198, -1608, 2208, -3194, 4290, -5550, 7480, -9906, 12672, -16648, 22038, -28344, 36641, -47796, 60801, -76624, 97710, -123216, 153362, -192954, 243072, -302028, 375639, -469122, 579486, -711432, 876864

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

Convolution inverse of A132130.

a(n) ~ (-1)^(n+1) * exp(2*Pi*sqrt(n/5)) / (2*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 31 2017

Empirical: Sum_{n>=1} a(n)/exp(2*Pi*n) = 19/2 + (5/2)*sqrt(5) - (1/2)*sqrt(450 + 206*sqrt(5)). - Simon Plouffe, Mar 02 2021

Mathematica

CoefficientList[Series[(QPochhammer[q] QPochhammer[q^10]/(QPochhammer[q^2] QPochhammer[q^5]))^6, {q, 0, 50}], q] (* Indranil Ghosh, Mar 30 2017 *)

Prog

(PARI) q='q+O('q^39); Vec((eta(q)*eta(q^10)/(eta(q^2)*eta(q^5)))^6) \\ Indranil Ghosh, Mar 31 2017

Crossrefs

Cf. A058097, A132130.

Sequence in context: A213791 A008440 A340962 * A022601 A112150 A240948

Adjacent sequences: A284626 A284627 A284628 * A284630 A284631 A284632

Keyword

sign

Author

Seiichi Manyama, Mar 30 2017

Status

approved