A289515 Expansion of 1/j^8 where j is the elliptic modular invariant (A000521).

1, -5952, 18352224, -39044962048, 64418979107376, -87832074172772736, 102995856743010218624, -106751551557580631373312, 99750353173835532264248472, -85298079996944806752079602240, 67533359025085585021484468850240, -49969584220872820552640845366351104, 34818371808714662813628963122182100160

Offset

8,2

Links

Seiichi Manyama, Table of n, a(n) for n = 8..414

Formula

a(n) ~ (-1)^n * 2^(3*k) * Pi^(12*k) * exp(Pi*sqrt(3)*n) * n^(3*k - 1) / (3^(3*k) * Gamma(1/3)^(18*k) * Gamma(3*k)), set k = 8. - Vaclav Kotesovec, Mar 07 2018

Mathematica

a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^8, {q, 0, n}]; Table[a[n], {n, 8, 20}] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Cf. A000521 (j).

1/j^k: A066395 (k=1), A288727 (k=2), A289454 (k=3), A289455 (k=4), A289512 (k=5), A289513 (k=6), A289514 (k=7), this sequence (k=8), A289516 (k=9), A289517 (k=10).

Sequence in context: A031755 A133598 A028517 * A186479 A266038 A032658

Adjacent sequences: A289512 A289513 A289514 * A289516 A289517 A289518

Keyword

sign

Author

Seiichi Manyama, Jul 07 2017

Status

approved