A299954 Coefficients in expansion of 432 * (j^(1/2) + (j - 1728)^(1/2)) / (j^(1/2) - (j - 1728)^(1/2)), where j is the j-function.

1, -120, 10260, -901120, 91676610, -10868097024, 1455225319640, -213263515975680, 33415165837622655, -5507368816607232000, 944071154093581913700, -166969055816397343457280, 30289678318291920442724670, -5611505834651089642200760320

Offset

-1,2

Links

Seiichi Manyama, Table of n, a(n) for n = -1..425

Wikipedia, Ramanujan-Sato series.

Formula

G.f.: 432 * (1 + (1 - 1728/j)^(1/2)) / (1 - (1 - 1728/j)^(1/2)).

G.f.: 432 * (E_4^(3/2) + E_6) / (E_4^(3/2) - E_6).

a(n) ~ -(-1)^n * 81 * Gamma(1/3)^9 * exp(Pi*sqrt(3)*n) / (2^(3/2) * Pi^(13/2) * n^(5/2)). - Vaclav Kotesovec, Apr 09 2018

Example

G.f.: 1/q - 120 + 10260*q - 901120*q^2 + 91676610*q^3 - 10868097024*q^4 + ...

Crossrefs

Cf. A000521, A004009 (E_4), A013973 (E_6), A299413, A299955 (E_4^(3/2)).

Sequence in context: A076005 A218503 A221620 * A226804 A104592 A135379

Adjacent sequences: A299951 A299952 A299953 * A299955 A299956 A299957

Keyword

sign

Author

Seiichi Manyama, Feb 22 2018

Status

approved