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E.g.f. A(x) satisfies A(x) = 1 + x * A(exp(x) - 1).
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%I #17 Dec 19 2015 13:10:01

%S 1,1,2,9,64,665,9366,170618,3885120,107728587,3563482900,138299564425,

%T 6211739264688,319190842232028,18581124650376484,1215078306042445710,

%U 88602560159713837728,7157866087368900148345,636974235270930297047526

%N E.g.f. A(x) satisfies A(x) = 1 + x * A(exp(x) - 1).

%H Vincenzo Librandi, <a href="/A048801/b048801.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n * A213357(n-1) if n>0. a(n+1) = (n+1) * Sum_{k=0..n} a(k) * stirling2(n, k). - _Michael Somos_, Jun 11 2012

%e 1 + x + 2*x^2 + 9*x^3 + 64*x^4 + 665*x^5 + 9366*x^6 + 170618*x^7 + 3885120*x^8 + ...

%t nmax=20; b = ConstantArray[0,nmax+1]; b[[1]]=1; Do[b[[n+2]] = (n+1)*Sum[b[[k+1]]*StirlingS2[n, k],{k,0,n}],{n,0,nmax-1}]; b (* _Vaclav Kotesovec_, Mar 12 2014 *)

%o (PARI) {a(n) = local(A); if( n<0, 0, A = 1 + O(x); for( k=1, n, A = 1 + x * subst( A, x, exp( x + A - A) - 1)); n! * polcoeff( A, n))} /* _Michael Somos_, Jun 11 2012 */

%Y Cf. A003659.

%K nonn,eigen

%O 0,3

%A _Christian G. Bower_, Mar 15 1999

%E Description corrected by _Michael Somos_