A288837 Coefficients in expansion of 691*E_12/Delta where Delta is the generating function of Ramanujan's tau function (A000594).

691, 82104, 136046844, 14852188160, 597231279270, 13989886672896, 230243024654600, 2938148100366336, 30857982903707085, 277430202679296000, 2194920198781034220, 15594068776929177600, 101032430846167832154, 604150780302870773760

Offset

-1,1

Links

Seiichi Manyama, Table of n, a(n) for n = -1..1000

Formula

a(n) = 691*A000521(n) = 691*A289063(n+1) for n > 0.

G.f.: 691*j - 432000 where j is the elliptic modular invariant.

a(n) ~ 691 * exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018

Mathematica

terms = 14;
E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];
691*E12[x]/QPochhammer[x]^24 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

Cf. A035230, A035281, A035293, A035314, A035315.

Cf. A000521 (j), A000594 (Delta), A029828 (691*E_12), A289063 (q*E_6^2/Delta), A289981.

Sequence in context: A135843 A130662 A029828 * A290049 A288989 A290009

Adjacent sequences: A288834 A288835 A288836 * A288838 A288839 A288840

Keyword

nonn

Author

Seiichi Manyama, Jul 17 2017

Status

approved