The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A299993

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A299993

Coefficients in expansion of (E_4^3/E_6^2)^(1/9).
(history; published version)

#18 by Vaclav Kotesovec at Sun Mar 04 12:38:13 EST 2018

STATUS

editing

approved

#17 by Vaclav Kotesovec at Sun Mar 04 12:36:32 EST 2018

FORMULA

a(n) * A299863(n) ~ -2*sin(2*Pi/9) * exp(4*Pi*n) / (9*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

STATUS

approved

editing

#16 by Vaclav Kotesovec at Sun Mar 04 11:42:36 EST 2018

STATUS

editing

approved

#15 by Vaclav Kotesovec at Sun Mar 04 11:34:12 EST 2018

FORMULA

a(n) ~ 2^(8/9) * Pi^(2/3) * exp(2*Pi*n) / (3^(1/9) * Gamma(2/9) * Gamma(1/4)^(8/9) * n^(7/9)). - Vaclav Kotesovec, Mar 04 2018

STATUS

approved

editing

#14 by Joerg Arndt at Wed Feb 28 12:46:14 EST 2018

STATUS

proposed

approved

#13 by Jean-François Alcover at Wed Feb 28 12:13:56 EST 2018

STATUS

editing

proposed

#12 by Jean-François Alcover at Wed Feb 28 12:13:52 EST 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)^(1/9) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 28 2018 *)

STATUS

approved

editing

#11 by Alois P. Heinz at Sun Feb 25 12:46:01 EST 2018

STATUS

proposed

approved

#10 by Seiichi Manyama at Sun Feb 25 10:03:55 EST 2018

STATUS

editing

proposed

#9 by Seiichi Manyama at Sun Feb 25 10:03:52 EST 2018

LINKS

Seiichi Manyama, <a href="/A299993/b299993.txt">Table of n, a(n) for n = 0..367</a>