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 A289319 #18 Mar 05 2018 05:13:16
%S A289319 1,210,-1260,232680,-28907970,4211355960,-671557897080,
%T A289319 113817372354240,-20151698294479500,3687092782592216970,
%U A289319 -692109989731133096760,132609267059636375116920,-25838624519733523814390760,5105657091664960508653858680
%N A289319 Coefficients in expansion of E_4^(7/8).
%C A289319 In general, for 0 < m < 1, the expansion of (E_4)^m is asymptotic to (-1)^(n+1) * m * 3^(2*m) * Gamma(1/3)^(18*m) * exp(Pi*sqrt(3)*n) / (2^(9*m) * Pi^(12*m) * Gamma(1-m) * n^(1+m)). - _Vaclav Kotesovec_, Mar 05 2018
%H A289319 Seiichi Manyama, <a href="/A289319/b289319.txt">Table of n, a(n) for n = 0..425</a>
%F A289319 G.f.: Product_{n>=1} (1-q^n)^(7*A110163(n)/8).
%F A289319 a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(15/8), where c = 7 * 3^(7/4) * Gamma(1/3)^(63/4) / (1024 * 2^(7/8) * Pi^(21/2) * Gamma(1/8)) = 0.1121182787986009012644546699220584282491804117887058146553161217384... - _Vaclav Kotesovec_, Jul 08 2017, updated Mar 05 2018
%t A289319 nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^(7/8), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)
%Y A289319 E_4^(k/8): A108091 (k=1), A289307 (k=2), A289308 (k=3), A289292 (k=4), A289309 (k=5), A289318 (k=6), this sequence (k=7).
%Y A289319 Cf. A004009 (E_4), A110163.
%K A289319 sign
%O A289319 0,2
%A A289319 _Seiichi Manyama_, Jul 02 2017