A299943 Coefficients in expansion of (E_4^3/E_6^2)^(1/36).

1, 48, 6912, 3479616, 1259268096, 575044765344, 253777092387840, 118545813515338368, 55748828845833043968, 26753648919849657887472, 12960874757914028815661568, 6344939709971525751086888640, 3129285552537639403735326646272

Offset

0,2

Links

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

Formula

Convolution inverse of A299422.

a(n) ~ c * exp(2*Pi*n) / n^(17/18), where c = 2^(2/9) * Pi^(1/6) / (3^(1/36) * Gamma(1/4)^(2/9) * Gamma(1/18)) = 0.0588537525900341685779220592527938... - Vaclav Kotesovec, Mar 04 2018

a(n) * A299422(n) ~ -sin(Pi/18) * exp(4*Pi*n) / (18*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

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)^(1/36) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 28 2018 *)

Crossrefs

(E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), A299696 (k=3), A299697 (k=4), A299698 (k=6), this sequence (k=8), A299949 (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), A299422.

Sequence in context: A233242 A266045 A130417 * A226257 A293094 A233199

Adjacent sequences: A299940 A299941 A299942 * A299944 A299945 A299946

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2018

Status

approved