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 A378469 #7 Nov 27 2024 10:04:59
%S A378469 1,-960,567360,-266138880,108735481920,-40500351480960,
%T A378469 14114830665358080,-4678563821426250240,1491145606587529742400,
%U A378469 -460511820740945555286720,138585483759128030100927360,-40812342463218781348220286720,11800049457060387849887324117760,-3358272262154871467174772417214080
%N A378469 Coefficients in expansion of (1/E_4)^4.
%C A378469 In general, for k > 0, the expansion of 1/(E_4)^k is asymptotic to (-1)^n * k * 2^(9*k) * Pi^(12*k) * n^(k-1) * exp(Pi*sqrt(3)*n) / (3^(2*k) * Gamma(1/3)^(18*k) * Gamma(k+1)).
%F A378469 a(n) ~ (-1)^n * 34359738368 * Pi^48 * n^3 * exp(Pi*sqrt(3)*n) / (19683 * Gamma(1/3)^72).
%t A378469 nmax = 20; CoefficientList[Series[(1+240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^(-4), {x, 0, nmax}], x]
%Y A378469 Cf. A001943 (k=1), A287933 (k=2), A378468 (k=3).
%Y A378469 Cf. A289566 (k=1/2), A295815 (k=1/4), A289247 (k=1/8).
%Y A378469 Cf. A004009, A289319.
%K A378469 sign
%O A378469 0,2
%A A378469 _Vaclav Kotesovec_, Nov 27 2024