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 A367470 #13 May 20 2025 02:28:41
%S A367470 1,4,28,268,3244,47404,810988,15891628,350851564,8615761324,
%T A367470 232911898348,6872755977388,219799913877484,7572909749244844,
%U A367470 279630706025296108,11016315458773541548,461211305514352065004,20448268640012928321964
%N A367470 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^2.
%F A367470 a(n) = Sum_{k=0..n} 2^k * (k+1)! * Stirling2(n,k).
%F A367470 a(0) = 1; a(n) = 2*Sum_{k=1..n} (k/n + 1) * binomial(n,k) * a(n-k).
%F A367470 a(0) = 1; a(n) = 4*a(n-1) - 3*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k).
%F A367470 a(n) ~ sqrt(2*Pi) * n^(n + 3/2) / (9 * log(3/2)^(n+2) * exp(n)). - _Vaclav Kotesovec_, May 20 2025
%o A367470 (PARI) a(n) = sum(k=0, n, 2^k*(k+1)!*stirling(n, k, 2));
%Y A367470 Cf. A004123, A367471.
%Y A367470 Cf. A005649, A367472.
%Y A367470 Cf. A367474.
%K A367470 nonn
%O A367470 0,2
%A A367470 _Seiichi Manyama_, Nov 19 2023