A289568 Coefficients in expansion of 1/E_10^(1/2).

1, 132, 93852, 35163744, 18119136156, 8462089683432, 4234179302847648, 2096050696254014016, 1057219212439789539228, 534730176137991079392036, 272470142855167873443179352, 139363825115618499934478625696

Offset

0,2

Links

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

Formula

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

a(n) ~ c * exp(2*Pi*n) / sqrt(n), where c = 0.4542595790370690606664796229968194763901027924111318430568304678613... = 2^(7/2) * Gamma(3/4)^12 / (3^(3/2) * Pi^(7/2)). - Vaclav Kotesovec, Jul 09 2017, updated Mar 07 2018

Mathematica

nmax = 20; CoefficientList[Series[(1 - 264*Sum[DivisorSigma[9, k]*x^k, {k, 1, nmax}])^(-1/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)

Crossrefs

1/E_k^(1/2): A289565 (k=2), A289566 (k=4), A289567 (k=6), A001943 (k=8), this sequence (k=10), A289569 (k=14).

Cf. A285836 (1/E_10), A289024, A289294 (E_10^(1/2)).

Sequence in context: A268098 A289294 A321975 * A368024 A114534 A147692

Adjacent sequences: A289565 A289566 A289567 * A289569 A289570 A289571

Keyword

nonn

Author

Seiichi Manyama, Jul 08 2017

Status

approved