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 A384523 #12 Jun 01 2025 10:02:06
%S A384523 1,4,44,708,15180,406884,13087404,491114628,21062220300,1016197112484,
%T A384523 54476506976364,3212426755972548,206654933095516620,
%U A384523 14401921040252826084,1080885666078491553324,86916516692600836638468,7455102038197447378720140,679412933203279242481083684
%N A384523 Expansion of e.g.f. 3/(7 - 4*exp(3*x)).
%H A384523 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384523 a(n) = (-3)^(n+1)/7 * Li_{-n}(7/4), where Li_{n}(x) is the polylogarithm function.
%F A384523 a(n) = 3^(n+1)/7 * Sum_{k>=0} k^n * (4/7)^k.
%F A384523 a(n) = Sum_{k=0..n} 4^k * 3^(n-k) * k! * Stirling2(n,k).
%F A384523 a(n) = (4/7) * Sum_{k=0..n} 7^k * (-3)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384523 a(0) = 1; a(n) = 4 * Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).
%F A384523 a(0) = 1; a(n) = 4 * a(n-1) + 7 * Sum_{k=1..n-1} (-3)^(k-1) * binomial(n-1,k) * a(n-k).
%o A384523 (PARI) a(n) = (-3)^(n+1)*polylog(-n, 7/4)/7;
%Y A384523 Cf. A094419, A384514, A384521, A384522, A384524.
%K A384523 nonn
%O A384523 0,2
%A A384523 _Seiichi Manyama_, Jun 01 2025