A289516 Expansion of 1/j^9 where j is the elliptic modular invariant (A000521).

1, -6696, 23137164, -54962170560, 100898554524030, -152570964293469792, 197804824654438091448, -226001211084270994392576, 232143871270380435422031645, -217638824689267205181123513840, 188440939272259782078293099295972

Offset

9,2

Links

Seiichi Manyama, Table of n, a(n) for n = 9..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 = 9. - Vaclav Kotesovec, Mar 07 2018

Mathematica

a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^9, {q, 0, n}]; Table[a[n], {n, 9, 19}] (* 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), this sequence (k=9), A289517 (k=10).

Sequence in context: A206008 A358869 A031846 * A239565 A234242 A252602

Adjacent sequences: A289513 A289514 A289515 * A289517 A289518 A289519

Keyword

sign

Author

Seiichi Manyama, Jul 07 2017

Status

approved