This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289247 #45 Nov 27 2024 04:13:31
%S A289247 1,-30,3780,-616440,111056910,-21135698280,4165203862440,
%T A289247 -840914061328320,172810940671692900,-35998781800053352710,
%U A289247 7579904611028433074280,-1609957152292592382408360,344417407415742189796786680,-74127324674775434904036905640
%N A289247 Coefficients in expansion of 1/E_4^(1/8).
%H A289247 Seiichi Manyama, <a href="/A289247/b289247.txt">Table of n, a(n) for n = 0..424</a>
%F A289247 G.f.: Product_{n>=1} (1-q^n)^(-A110163(n)/8).
%F A289247 a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(7/8), where c = Pi^(3/2) / (2^(15/8) * 3^(1/4) * Gamma(1/3)^(9/4) * Gamma(9/8)) = 0.133402757019143151407904538533... - _Vaclav Kotesovec_, Jul 09 2017, updated Mar 05 2018
%F A289247 a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A300147(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Feb 27 2018
%t A289247 nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^(-1/8), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 09 2017 *)
%Y A289247 E_4^(k/8): A001943 (k=-8), A289566 (k=-4), A295815 (k=-2), this sequence (k=-1), A108091 (k=1), A289307 (k=2), A289308 (k=3), A289292 (k=4), A289309 (k=5), A289318 (k=6), A289319 (k=7), A004009 (k=8).
%Y A289247 Cf. A110163, A300147.
%K A289247 sign
%O A289247 0,2
%A A289247 _Seiichi Manyama_, Jul 08 2017