A289392 Coefficients in expansion of E_2^(1/4).

1, -6, -72, -1104, -20238, -405792, -8601840, -189317568, -4281478272, -98841343686, -2318973049008, -55118876238000, -1324194430710912, -32099173821105312, -784045854628721568, -19276683937074656064, -476644852188898489662

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..702

Formula

G.f.: Product_{n>=1} (1-q^n)^A289394(n).

a(n) ~ c / (n^(5/4) * r^n), where r = A211342 = 0.03727681029645165815098078565... is the root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24 and c = -0.209452682241344640265132676904094736935029272937832600102950644347... - Vaclav Kotesovec, Jul 08 2017

G.f.: Sum_{k>=0} A004984(k) * (3*f(q))^k where f(q) is Sum_{k>=1} sigma_1(k)*q^k. - Seiichi Manyama, Jun 16 2018

Mathematica

nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[1, k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Crossrefs

E_2^(k/4): this sequence (k=1), A289291 (k=2), A289393 (k=3).

E_k^(1/4): this sequence (k=2), A289307 (k=4), A289326 (k=6), A289292 (k=8), A110150 (k=10), A289391 (k=14).

Cf. A004984, A006352 (E_2), A108091, A109817, A289394.

Sequence in context: A052678 A052719 A196882 * A272688 A063965 A347023

Adjacent sequences: A289389 A289390 A289391 * A289393 A289394 A289395

Keyword

sign

Author

Seiichi Manyama, Jul 05 2017

Status

approved