OFFSET
0,2
FORMULA
O.g.f.: Sum_{n>=0} 3^n*x^n/(1 - (n+1)*x)^(n+1).
E.g.f.: exp(x + 3*x*exp(x)).
MATHEMATICA
Table[Sum[Binomial[n, k]3^k (k+1)^(n-k), {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Nov 12 2012 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*3^k*(k+1)^(n-k))}
(PARI) {a(n)=polcoeff(sum(m=0, n, 3^m*x^m/(1-(m+1)*x+x*O(x^n))^(m+1)), n)}
(PARI) {a(n)=n!*polcoeff(exp(x+3*x*exp(x+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 06 2011
STATUS
approved