A289569 - OEIS

%I #17 Mar 07 2018 04:12:08

%S 1,12,98532,22675584,16099478436,6580135809432,3539736295913088,

%T 1699883073000957696,871767496424764386468,438331617201642108107916,

%U 224266585355757815798085192,114622723650418140746841457536,58945651172799536532104421386880

%N Coefficients in expansion of 1/E_14^(1/2).

%H Seiichi Manyama, <a href="/A289569/b289569.txt">Table of n, a(n) for n = 0..367</a>

%F G.f.: Product_{n>=1} (1-q^n)^(-A289029(n)/2).

%F a(n) ~ c * exp(2*Pi*n) / sqrt(n), where c = 0.3764946174077880880364705796802173599460310621830541667074693852949... = 2^(9/2) * Gamma(3/4)^16 / (9 * Pi^(9/2)). - _Vaclav Kotesovec_, Jul 09 2017, updated Mar 07 2018

%t nmax = 20; CoefficientList[Series[(1 - 24*Sum[DivisorSigma[13, k]*x^k, {k, 1, nmax}])^(-1/2), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)

%Y 1/E_k^(1/2): A289565 (k=2), A289566 (k=4), A289567 (k=6), A001943 (k=8), A289568 (k=10), this sequence (k=14).

%Y Cf. A287964 (1/E_14), A289029, A289295 (E_14^(1/2)).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 08 2017