A296609 Coefficients in expansion of (E_6^2/E_4^3)^(1/144).

1, -12, -1368, -779184, -260251104, -120710392488, -51881715871776, -24129355507367136, -11210568318996090624, -5342692661136883228860, -2567906908021088206807248, -1249094126109188331384940944, -612254304549600491293149962880

Offset

0,2

Links

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

Formula

G.f.: (1 - 1728/j)^(1/144).

a(n) ~ -Gamma(1/4)^(1/18) * exp(2*Pi*n) / (24 * 2^(1/18) * 3^(143/144) * Pi^(1/24) * Gamma(71/72) * n^(73/72)). - Vaclav Kotesovec, Mar 04 2018

a(n) * A299694(n) ~ -sin(Pi/72) * exp(4*Pi*n) / (72*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}];
(E6[x]^2/E4[x]^3)^(1/144) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

(E_6^2/E_4^3)^(k/288): A289366 (k=1), this sequence (k=2), A296614 (k=3), A296652 (k=4), A297021 (k=6), A299422 (k=8), A299862 (k=9), A289368 (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j), A299694.

Sequence in context: A007943 A015512 A004145 * A171484 A230519 A235535

Adjacent sequences: A296606 A296607 A296608 * A296610 A296611 A296612

Keyword

sign

Author

Seiichi Manyama, Feb 15 2018

Status

approved