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a(n+1) = Sum_{k=0..n} (n!/k!)*binomial(n,k)*a(k).
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%I #8 Aug 13 2019 20:51:55

%S 1,1,2,8,50,442,5212,78664,1472756,33378740,898227944,28253387104,

%T 1025373023848,42467845178632,1988513519453360,104413376937507488,

%U 6104596110052561808,394921638012548722576,28112685278602155590944,2191142414957886078590080

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

%H Alois P. Heinz, <a href="/A110083/b110083.txt">Table of n, a(n) for n = 0..307</a>

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p a(n-i)*binomial(n-1, i-1)^2*(i-1)!, i=1..n))

%p end:

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 13 2019

%t nmax=20; b = ConstantArray[0,nmax+2]; b[[1]]=1; Do[b[[n+2]] = Sum[n!/k!*Binomial[n,k]*b[[k+1]],{k,0,n}],{n,0,nmax}]; b (* _Vaclav Kotesovec_, Mar 02 2014 *)

%Y Cf. A001063.

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, Sep 04 2005