A294976 Coefficients in expansion of (E_6/E_2^6)^(1/12).

1, -30, -11340, -3912600, -1520905170, -636170644008, -278687199310200, -126000360658968000, -58290111778749466140, -27440829122946510954630, -13096614404248661886145848, -6320198941502349713305002120, -3077986352751848627729986859400

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: Product_{n>=1} (1-q^n)^A294975(n).

a(n) ~ -Gamma(1/3)^2 * Gamma(1/4)^(10/3) * exp(2*Pi*n) / (16 * 2^(1/12) * 3^(7/12) * Pi^(5/2) * Gamma(1/12) * n^(13/12)). - Vaclav Kotesovec, Jun 03 2018

Equivalently, a(n) ~ -Gamma(1/3) * Gamma(1/4)^(7/3) * exp(2*Pi*n) / (2^(23/6) * 3^(23/24) * Pi^2 * sqrt(1 + sqrt(3)) * n^(13/12)). - Vaclav Kotesovec, Nov 26 2024

Mathematica

terms = 13;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E6[x]/E2[x]^6)^(1/12) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

Cf. A109817, A289565, A294974, A294975.

Sequence in context: A056071 A299410 A377221 * A294975 A294979 A250435

Adjacent sequences: A294973 A294974 A294975 * A294977 A294978 A294979

Keyword

sign

Author

Seiichi Manyama, Feb 12 2018

Status

approved