A305886 Expansion of (1 - 1728*x)^(1/288).

1, -6, -5166, -5940900, -7690495050, -10622111763060, -15285218827043340, -22626491069403298440, -34194284628635734767450, -52499624999832064779624900, -81615917024738927906404869540, -128166668244121840059567065130360

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..310

Formula

a(n) = 6^n/n! * Product_{k=0..n-1} (288*k - 1) for n > 0.

a(n) = -1728^n * Gamma(n - 1/288) / (288 * Gamma(287/288) * Gamma(n+1)). - Vaclav Kotesovec, Jun 14 2018

a(n) ~ -2^(6*n - 5) * 3^(3*n - 2) / (Gamma(287/288) * n^(289/288)). - Vaclav Kotesovec, Jun 16 2018

D-finite with recurrence: n*a(n) +6*(-288*n+289)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

Prog

(PARI) N=20; x='x+O('x^N); Vec((1-1728*x)^(1/288))

Crossrefs

Cf. A004996, A289366.

Sequence in context: A343096 A066061 A028366 * A115431 A116117 A116135

Adjacent sequences: A305883 A305884 A305885 * A305887 A305888 A305889

Keyword

sign

Author

Seiichi Manyama, Jun 13 2018

Status

approved