A289517 Expansion of 1/j^10 where j is the elliptic modular invariant (A000521).

1, -7440, 28475640, -74704723520, 151031520191580, -250835888956579488, 356272260416109602240, -444864441668603737630080, 498241081014831011965132710, -508187364230945384698554319920, 477695553082956543572082694287840

Offset

10,2

Links

Seiichi Manyama, Table of n, a(n) for n = 10..413

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 = 10. - Vaclav Kotesovec, Mar 07 2018

Mathematica

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

Sequence in context: A360355 A324897 A051259 * A178281 A250971 A250239

Adjacent sequences: A289514 A289515 A289516 * A289518 A289519 A289520

Keyword

sign

Author

Seiichi Manyama, Jul 07 2017

Status

approved