A028513 Expansion of A007245^4.

1, 992, 385520, 73424000, 7032770680, 330234251072, 9708251628992, 205208814844160, 3384709979113500, 45920987396301280, 531402725344000864, 5384625599438260096, 48726640432968418240, 399835655086212744000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A000521 (j(q)).

(q*j(q))^(k/24): A289397 (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12), A028512 (k=16), this sequence (k=32), A028514 (k=40), A028515 (k=48).

Programs

Mathematica

CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^4, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 15 2017 *)

Formula

(q*j(q))^(4/3) where j(q) is the elliptic modular invariant. - Seiichi Manyama, Jul 15 2017

a(n) ~ exp(8*Pi*sqrt(n/3)) / (3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jul 15 2017