A109817 G.f.: 12th root of Eisenstein series E_6 (cf. A013973).

1, -42, -11088, -3774624, -1472710974, -617481728640, -270883381218912, -122585272771463040, -56747118995519331456, -26727350506044696990762, -12760853360973370821796320, -6159994719956314185540737376, -3000691311646502407278581263104, -1472883416501251994527873967792256

Offset

0,2

Links

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

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Formula

G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/12). - Seiichi Manyama, Jul 02 2017

a(n) ~ c * exp(2*Pi*n) / n^(13/12), where c = -Gamma(1/4)^(10/3) * Gamma(1/3)^2 / (16 * 6^(1/12) * Pi^3 * Gamma(1/12)) = -0.079329971529325538458906713053582098... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A299503(k)*a(n-k) for n > 0. - Seiichi Manyama, Feb 27 2018

G.f.: Sum_{k>=0} A303055(k) * f(q)^k where f(q) is Sum_{k>=1} sigma_5(k)*q^k. - Seiichi Manyama, Jun 15 2018

Mathematica

nmax = 20; s = 6; CoefficientList[Series[(1 - 2*s/BernoulliB[s] * Sum[DivisorSigma[s - 1, k]*x^k, {k, 1, nmax}])^(1/12), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 02 2017 *)

Crossrefs

E_6^(k/12): this sequence (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).

Cf. A001160, A013973, A288851, A299503, A303055.

Sequence in context: A006699 A303055 A226262 * A211909 A289396 A159417

Adjacent sequences: A109814 A109815 A109816 * A109818 A109819 A109820

Keyword

sign

Author

N. J. A. Sloane, Sep 15 2005

Status

approved