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 A377965 #14 Nov 23 2024 12:23:02
%S A377965 1,3,11,55,309,1931,13543,101991,828425,7192819,66002691,639830423,
%T A377965 6510397501,69266297595,768989536799,8876171274631,106301772962193,
%U A377965 1318277355041891,16892429768517115,223330116792810999,3041570471301007301,42611228176879105003
%N A377965 Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^2).
%F A377965 a(n) = n! * Sum_{k=0..n} binomial(2*k+2,n-k) / k!.
%F A377965 From _Vaclav Kotesovec_, Nov 23 2024: (Start)
%F A377965 Recurrence: (n^2 - 3*n + 4)*a(n) = (n^2 - 3*n + 8)*a(n-1) + 2*(n-1)*(2*n^2 - 5*n + 4)*a(n-2) + 3*(n-2)*(n-1)*(n^2 - n + 2)*a(n-3).
%F A377965 a(n) ~ 3^(n/3 - 7/6) * exp(-4/81 + 3^(-7/3)*n^(1/3) + 2*3^(-2/3)*n^(2/3) - 2*n/3) * n^(2*(n+1)/3) * (1 + 5813*3^(1/3)/(4374*n^(1/3))). (End)
%o A377965 (PARI) a(n, s=2, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
%Y A377965 Cf. A377954, A377966.
%Y A377965 Cf. A361278, A377963.
%Y A377965 Cf. A343884.
%K A377965 nonn,easy
%O A377965 0,2
%A A377965 _Seiichi Manyama_, Nov 12 2024