A048801 E.g.f. A(x) satisfies A(x) = 1 + x * A(exp(x) - 1).

1, 1, 2, 9, 64, 665, 9366, 170618, 3885120, 107728587, 3563482900, 138299564425, 6211739264688, 319190842232028, 18581124650376484, 1215078306042445710, 88602560159713837728, 7157866087368900148345, 636974235270930297047526

Offset: 0

Author

Christian G. Bower, Mar 15 1999

Keywords

• nonn
• eigen

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A003659.

Programs

Mathematica

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 *)

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 */

Formula

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

Extensions

Description corrected by Michael Somos