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 A382753 #18 Jun 03 2025 08:43:08
%S A382753 1,2,14,138,1806,29562,580734,13309578,348611886,10272416922,
%T A382753 336326121054,12112707922218,475894244100366,20255443904321082,
%U A382753 928448378212678974,45597074777924954058,2388608236671667179246,132947999835258872046042,7835059049893316949502494
%N A382753 Expansion of e.g.f. 3/(5 - 2*exp(3*x)).
%H A382753 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A382753 a(n) = (-3)^(n+1)/5 * Li_{-n}(5/2), where Li_{n}(x) is the polylogarithm function.
%F A382753 a(n) = 3^(n+1)/5 * Sum_{k>=0} k^n * (2/5)^k.
%F A382753 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * k! * Stirling2(n,k).
%F A382753 a(n) = (2/5) * A201367(n) = (2/5) * Sum_{k=0..n} 5^k * (-3)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A382753 a(0) = 1; a(n) = 2 * Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).
%F A382753 a(0) = 1; a(n) = 2 * a(n-1) + 5 * Sum_{k=1..n-1} (-3)^(k-1) * binomial(n-1,k) * a(n-k).
%o A382753 (PARI) a(n) = (-3)^(n+1)*polylog(-n, 5/2)/5;
%Y A382753 Cf. A094417, A326324, A384435.
%Y A382753 Cf. A004123, A216794, A384521.
%Y A382753 Cf. A201367.
%K A382753 nonn
%O A382753 0,2
%A A382753 _Seiichi Manyama_, Jun 03 2025