A289514 Expansion of 1/j^7 where j is the elliptic modular invariant (A000521).

1, -5208, 14120820, -26541267200, 38855720054130, -47202347794186368, 49508378454093937112, -46064135137842011274240, 38772486464181493598745975, -29962343460442400908618822720, 21503606192545582819121286031524

Offset

7,2

Links

Seiichi Manyama, Table of n, a(n) for n = 7..415

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 = 7. - Vaclav Kotesovec, Mar 07 2018

Mathematica

a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^7, {q, 0, n}]; Table[a[n], {n, 7, 17}] (* 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), this sequence (k=7), A289515 (k=8), A289516 (k=9), A289517 (k=10).

Sequence in context: A165599 A109159 A231113 * A031616 A067224 A204139

Adjacent sequences: A289511 A289512 A289513 * A289515 A289516 A289517

Keyword

sign

Author

Seiichi Manyama, Jul 07 2017

Status

approved