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A299696 Coefficients in expansion of (E_4^3/E_6^2)^(1/96). 19
1, 18, 2322, 1234116, 430292646, 197681749128, 86165040337452, 40145493017336976, 18768723217958523222, 8975036477140737601806, 4331009172188712335053032, 2113419430011730408087143924, 1039122180212218474089489166980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..368

FORMULA

Convolution inverse of A296614.

a(n) ~ 2^(1/12) * Pi^(1/16) * exp(2*Pi*n) / (3^(1/96) * Gamma(1/48) * Gamma(1/4)^(1/12) * n^(47/48)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A296614(n) ~ -sin(Pi/48) * exp(4*Pi*n) / (48*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)^(1/96) + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 26 2018 *)

CROSSREFS

(E_4^3/E_6^2)^(k/288): A289365 (k=1), A299694 (k=2), this sequence (k=3), A299697 (k=4), A299698 (k=6), A299943 (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), A296614.

Sequence in context: A136834 A279296 A327266 * A282830 A174637 A267065

Adjacent sequences:  A299693 A299694 A299695 * A299697 A299698 A299699

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 16 2018

STATUS

approved

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Last modified February 27 11:04 EST 2021. Contains 341649 sequences. (Running on oeis4.)