A110083 a(n+1) = Sum_{k=0..n} (n!/k!)*binomial(n,k)*a(k).

1, 1, 2, 8, 50, 442, 5212, 78664, 1472756, 33378740, 898227944, 28253387104, 1025373023848, 42467845178632, 1988513519453360, 104413376937507488, 6104596110052561808, 394921638012548722576, 28112685278602155590944, 2191142414957886078590080

Offset: 0

Author

Vladeta Jovovic, Sep 04 2005

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..307

Crossrefs

Cf. A001063.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-i)*binomial(n-1, i-1)^2*(i-1)!, i=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 13 2019

Mathematica

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 *)

Formula

Conjecture: a(n) = R(n,0) where R(n,k) = R(n-1,n-1) + n * Sum_{j=0..k-1} R(n-1,j) for 0 <= k <= n with R(0,0) = 1. - Mikhail Kurkov, Jul 18 2025