A289512 Expansion of 1/j^5 where j is the elliptic modular invariant (A000521).

1, -3720, 7318620, -10127095360, 11061866004390, -10151440298355744, 8136148305855926840, -5846643254165797186560, 3838606195380374717418465, -2335284727373310897029544400, 1330851094413644423959537571652, -716606026961666494353690542814720

Offset

5,2

Links

Seiichi Manyama, Table of n, a(n) for n = 5..417

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 = 5. - Vaclav Kotesovec, Mar 07 2018

Mathematica

a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^5, {q, 0, n}]; Table[a[n], {n, 5, 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), this sequence (k=5), A289513 (k=6), A289514 (k=7), A289515 (k=8), A289516 (k=9), A289517 (k=10).

Sequence in context: A252421 A296908 A237736 * A260860 A221013 A224436

Adjacent sequences: A289509 A289510 A289511 * A289513 A289514 A289515

Keyword

sign

Author

Seiichi Manyama, Jul 07 2017

Status

approved