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A289515 Expansion of 1/j^8 where j is the elliptic modular invariant (A000521). 7
1, -5952, 18352224, -39044962048, 64418979107376, -87832074172772736, 102995856743010218624, -106751551557580631373312, 99750353173835532264248472, -85298079996944806752079602240, 67533359025085585021484468850240, -49969584220872820552640845366351104, 34818371808714662813628963122182100160 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 18 04:54 EDT 2019. Contains 328145 sequences. (Running on oeis4.)