A289308 - OEIS

%I #17 Mar 05 2018 04:27:56

%S 1,90,-5940,758520,-115431930,19355028840,-3447208777320,

%T 639751846440960,-122326632902618100,23925871041887048130,

%U -4763590542726586318440,962102309316632909723880,-196619722885250960565506040,40580696990507644723354537320

%N Coefficients in expansion of E_4^(3/8).

%H Seiichi Manyama, <a href="/A289308/b289308.txt">Table of n, a(n) for n = 0..424</a>

%F G.f.: Product_{n>=1} (1-q^n)^(3*A110163(n)/8).

%F a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(11/8), where c = 3^(7/4) * Gamma(1/3)^(27/4) / (64 * 2^(3/8) * Pi^(9/2) * Gamma(5/8)) = 0.2574920621515873836544977885672468081360882154861344422709504189964... - _Vaclav Kotesovec_, Jul 09 2017, updated Mar 05 2018

%t nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^(3/8), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y E_4^(k/8): A108091 (k=1), A289307 (k=2), this sequence (k=3), A289292 (k=4), A289309 (k=5), A289318 (k=6), A289319 (k=7).

%Y Cf. A004009 (E_4), A110163.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 02 2017