A289513 - OEIS

A289513

Expansion of 1/j^6 where j is the elliptic modular invariant (A000521).

1, -4464, 10442952, -17039255232, 21778105580100, -23220214437622752, 21481529172149572992, -17710788549056167790208, 13266671900249257490243610, -9160802613358728056593238800, 5897060690397181329853257045696

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OFFSET

6,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 6..416

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 = 6. - Vaclav Kotesovec, Mar 07 2018

MATHEMATICA

a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^6, {q, 0, n}]; Table[a[n], {n, 6, 16}] (* 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), this sequence (k=6), A289514 (k=7), A289515 (k=8), A289516 (k=9), A289517 (k=10).

Sequence in context: A185767 A089202 A250977 * A345590 A345848 A221007

Adjacent sequences: A289510 A289511 A289512 * A289514 A289515 A289516

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 07 2017

STATUS

approved