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 A384514 #29 Jun 01 2025 09:57:47
%S A384514 1,1,8,78,960,14736,272448,5881968,145105920,4026744576,124159039488,
%T A384514 4211132779008,155814875873280,6245695887446016,269610827961212928,
%U A384514 12469729905669224448,615184657168540631040,32246522356406129197056,1789714914567248392224768
%N A384514 Expansion of e.g.f. 6/(7 - exp(6*x)).
%H A384514 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384514 a(n) = (-6)^(n+1)/7 * Li_{-n}(7), where Li_{n}(x) is the polylogarithm function.
%F A384514 a(n) = 6^(n+1) * Sum_{k>=0} k^n * (1/7)^(k+1).
%F A384514 a(n) = Sum_{k=0..n} 6^(n-k) * k! * Stirling2(n,k).
%F A384514 a(n) = (1/7) * Sum_{k=0..n} 7^k * (-6)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384514 a(0) = 1; a(n) = Sum_{k=1..n} 6^(k-1) * binomial(n,k) * a(n-k).
%F A384514 a(0) = 1; a(n) = a(n-1) + 7 * Sum_{k=1..n-1} (-6)^(k-1) * binomial(n-1,k) * a(n-k).
%o A384514 (PARI) a(n) = (-6)^(n+1)*polylog(-n, 7)/7;
%Y A384514 Cf. A326323.
%Y A384514 Cf. A094419, A384521, A384522, A384523, A384524.
%K A384514 nonn
%O A384514 0,3
%A A384514 _Seiichi Manyama_, Jun 01 2025