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 A384524 #17 Jun 04 2025 07:10:34
%S A384524 1,5,60,1070,25440,756080,26964960,1121963120,53351831040,
%T A384524 2854122433280,169649803023360,11092432778385920,791204615734640640,
%U A384524 61138238969353748480,5087702653663698677760,453621615686933964830720,43141424825262182799114240,4359374368561019960377671680
%N A384524 Expansion of e.g.f. 2/(7 - 5*exp(2*x)).
%H A384524 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F A384524 a(n) = (-2)^(n+1)/7 * Li_{-n}(7/5), where Li_{n}(x) is the polylogarithm function.
%F A384524 a(n) = 2^(n+1)/7 * Sum_{k>=0} k^n * (5/7)^k.
%F A384524 a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * k! * Stirling2(n,k).
%F A384524 a(n) = (5/7) * Sum_{k=0..n} 7^k * (-2)^(n-k) * k! * Stirling2(n,k) for n > 0.
%F A384524 a(0) = 1; a(n) = 5 * Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k).
%F A384524 a(0) = 1; a(n) = 5 * a(n-1) + 7 * Sum_{k=1..n-1} (-2)^(k-1) * binomial(n-1,k) * a(n-k).
%p A384524 A384524:=proc(n)
%p A384524 add(5^k * 2^(n-k) * k! * combinat[stirling2](n,k) ,k=0..n) ;
%p A384524 end proc:
%p A384524 seq(A384524(n), n=0..40); # _R. J. Mathar_, Jun 04 2025
%o A384524 (PARI) a(n) = (-2)^(n+1)*polylog(-n, 7/5)/7;
%Y A384524 Cf. A094419, A384514, A384521, A384522, A384523.
%K A384524 nonn
%O A384524 0,2
%A A384524 _Seiichi Manyama_, Jun 01 2025