A377963 - OEIS

%I #12 Nov 13 2024 06:46:33

%S 1,2,7,34,173,1066,7147,51962,412729,3478258,31220111,296409202,

%T 2953487077,30870965594,336796018483,3824230997386,45114077004017,

%U 551338045973602,6968344940992279,90931562913957698,1222939213021853341,16929504703420184842,240909000856701880187

%N Expansion of e.g.f. (1+x) * exp(x*(1+x)^2).

%F a(n) = n! * Sum_{k=0..n} binomial(2*k+1,n-k) / k!.

%F a(n) = a(n-1) + (4*n-3)*a(n-2) + 3*(n-2)*n*a(n-3) for n > 2.

%o (PARI) a(n, s=1, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);

%Y Cf. A018191, A377964.

%Y Cf. A361278, A377965.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Nov 12 2024