A377963 Expansion of e.g.f. (1+x) * exp(x*(1+x)^2).
1, 2, 7, 34, 173, 1066, 7147, 51962, 412729, 3478258, 31220111, 296409202, 2953487077, 30870965594, 336796018483, 3824230997386, 45114077004017, 551338045973602, 6968344940992279, 90931562913957698, 1222939213021853341, 16929504703420184842, 240909000856701880187
Offset: 0
Programs
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PARI
a(n, s=1, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} binomial(2*k+1,n-k) / k!.
a(n) = a(n-1) + (4*n-3)*a(n-2) + 3*(n-2)*n*a(n-3) for n > 2.