A289294 Coefficients in expansion of E_10^(1/2).

1, -132, -76428, -12686784, -4629945804, -1581036186312, -643032851554368, -264454897726360704, -114830224962140965068, -50847479367845783084484, -23070238839261012248537688, -10629338992044523324726971456

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Links

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

Crossrefs

E_k^(1/2): A289291 (k=2), A289292 (k=4), A289293 (k=6), A004009 (k=8), this sequence (k=10), A289295 (k=14).

Cf. A013974 (E_10), A289024.

Programs

Mathematica

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

Formula

G.f.: Product_{n>=1} (1-q^n)^(A289024(n)/2).

a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -3^(3/2) * Pi^(5/2) / (2^(9/2) * Gamma(3/4)^12) = -0.3503612261281732359954402284478780636268623476628... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018