OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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
EXAMPLE
1 + x + 2*x^2 + 9*x^3 + 64*x^4 + 665*x^5 + 9366*x^6 + 170618*x^7 + 3885120*x^8 + ...
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 *)
PROG
(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 */
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Mar 15 1999
EXTENSIONS
Description corrected by Michael Somos
STATUS
approved
