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 A367471 #10 Nov 19 2023 08:25:07
%S A367471 1,6,54,630,8982,150966,2918934,63772470,1552910742,41690570166,
%T A367471 1223096629014,38924237638710,1335418262833302,49129420920630966,
%U A367471 1929262811804022294,80540656071983191350,3561781875173605408662,166331104582900651581366
%N A367471 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^3.
%F A367471 a(n) = (1/2) * Sum_{k=0..n} 2^k * (k+2)! * Stirling2(n,k).
%F A367471 a(0) = 1; a(n) = 2*Sum_{k=1..n} (2*k/n + 1) * binomial(n,k) * a(n-k).
%F A367471 a(0) = 1; a(n) = 6*a(n-1) - 3*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).
%o A367471 (PARI) a(n) = sum(k=0, n, 2^k*(k+2)!*stirling(n, k, 2))/2;
%Y A367471 Cf. A004123, A367470.
%Y A367471 Cf. A226515, A367473.
%K A367471 nonn
%O A367471 0,2
%A A367471 _Seiichi Manyama_, Nov 19 2023