A299949 Coefficients in expansion of (E_4^3/E_6^2)^(1/32).

1, 54, 7938, 3958956, 1442594502, 658201268952, 291148964582796, 136084851675471024, 64069809910723011222, 30769281599576554087722, 14917804015099613922436392, 7307669924831130556163175612, 3606311646826590340455185471940

Offset: 0

Author

Seiichi Manyama, Feb 22 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..367

Crossrefs

(E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), A299697 (k=4), A299698 (k=6), A299943 (k=8), this sequence (k=9), A289369 (k=12), A299950 (k=16), A299951 (k=18), A299953 (k=24), A299993 (k=32), A299994 (k=36), A300052 (k=48), A300053 (k=72), A300054 (k=96), A300055 (k=144), A289209 (k=288).

Cf. A004009 (E_4), A013973 (E_6), A299862.

Programs

Mathematica

terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E4[x]^3/E6[x]^2)^(1/32) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 28 2018 *)

Formula

Convolution inverse of A299862.

a(n) ~ c * exp(2*Pi*n) / n^(15/16), where c = 2^(1/4) * Pi^(3/16) / (3^(1/32) * Gamma(1/4)^(1/4) * Gamma(1/16)) = 0.06666699751397812787469360011212565... - Vaclav Kotesovec, Mar 04 2018

a(n) * A299862(n) ~ -sin(Pi/16) * exp(4*Pi*n) / (16*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018