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 A377963 #12 Nov 13 2024 06:46:33
%S A377963 1,2,7,34,173,1066,7147,51962,412729,3478258,31220111,296409202,
%T A377963 2953487077,30870965594,336796018483,3824230997386,45114077004017,
%U A377963 551338045973602,6968344940992279,90931562913957698,1222939213021853341,16929504703420184842,240909000856701880187
%N A377963 Expansion of e.g.f. (1+x) * exp(x*(1+x)^2).
%F A377963 a(n) = n! * Sum_{k=0..n} binomial(2*k+1,n-k) / k!.
%F A377963 a(n) = a(n-1) + (4*n-3)*a(n-2) + 3*(n-2)*n*a(n-3) for n > 2.
%o A377963 (PARI) a(n, s=1, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
%Y A377963 Cf. A018191, A377964.
%Y A377963 Cf. A361278, A377965.
%K A377963 nonn,easy
%O A377963 0,2
%A A377963 _Seiichi Manyama_, Nov 12 2024