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E.g.f. satisfies A'(x) = A(x/(1-x)).
5

%I #25 Apr 10 2018 02:36:35

%S 1,1,1,3,15,111,1131,15081,253473,5220225,128886921,3749014251,

%T 126648293391,4909623331023,216189866951235,10718939718977121,

%U 593865369943409601,36520856568972350721,2478236630512178688273,184588566642520989171795,15020141103053997234030351

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

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

%H Alois P. Heinz, <a href="/A001063/b001063.txt">Table of n, a(n) for n = 0..300</a>

%H P. J. Cameron, <a href="http://dx.doi.org/10.1016/0024-3795(95)00352-R">Sequence operators from groups</a>, Linear Alg. Applic., 226-228 (1995), 109-113.

%F a(n+1) = Sum_{k=0..n} n!/k!*binomial(n-1, k-1)*a(k). - _Vladeta Jovovic_, Sep 03 2005

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

%p (n-1)!/k!*binomial(n-2, k-1)*a(k), k=0..n-1))

%p end:

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 10 2015

%t 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 *)

%K nonn,eigen

%O 0,4

%A _Peter J. Cameron_

%E More terms from _Christian G. Bower_, Mar 15 1999