A110150 G.f.: 4th root of Eisenstein series E_10 (cf. A013974).

1, -66, -40392, -9009264, -3725341158, -1400292801072, -604993149612720, -262280205541007808, -118717180239835505592, -54520207050101542651506, -25525844887805197307977968, -12095360676632550886664063760, -5797006133905562955666277287792, -2803076705590018145443840156918512

Offset: 0

Author

N. J. A. Sloane, Sep 15 2005

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..360
• 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.

Crossrefs

E_k^(1/4): A289392 (k=2), A289307 (k=4), A289326 (k=6), A289292 (k=8), this sequence (k=10), A289391 (k=14).

Cf. A004984, A013974, A109817, A289294.

Programs

Mathematica

nmax = 20; s = 10; CoefficientList[Series[(1 - 2*s/BernoulliB[s] * Sum[DivisorSigma[s - 1, k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 02 2017 *)

Formula

a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -3^(3/4) * Pi^(3/2) / (2^(15/4) * Gamma(3/4)^7) = -0.227361380713650977567497769428903183591275821407342369621... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018

G.f.: Sum_{k>=0} A004984(k) * (33*f(q))^k where f(q) is Sum_{k>=1} sigma_9(k)*q^k. - Seiichi Manyama, Jun 16 2018