A001063 E.g.f. satisfies A'(x) = A(x/(1-x)).

1, 1, 1, 3, 15, 111, 1131, 15081, 253473, 5220225, 128886921, 3749014251, 126648293391, 4909623331023, 216189866951235, 10718939718977121, 593865369943409601, 36520856568972350721, 2478236630512178688273, 184588566642520989171795, 15020141103053997234030351

Offset: 0

Author

Peter J. Cameron

Keywords

• nonn
• eigen

Comments

Sequence shifts left when x is replaced by x/(1-x) in e.g.f.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• P. J. Cameron, Sequence operators from groups, Linear Alg. Applic., 226-228 (1995), 109-113.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      (n-1)!/k!*binomial(n-2, k-1)*a(k), k=0..n-1))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 10 2015

Mathematica

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

Formula

a(n+1) = Sum_{k=0..n} n!/k!*binomial(n-1, k-1)*a(k). - Vladeta Jovovic, Sep 03 2005

Extensions

More terms from Christian G. Bower, Mar 15 1999