OFFSET
0,3
FORMULA
G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*k(k+1)/2*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.
EXAMPLE
G.f.: A(x) = 1 + x + 7*x^2 + 37*x^3 + 245*x^4 + 2094*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^n*3*x^2 + 3^n*6*x^3 +...]^n/n.
D^n x/(1-x)^3 = x + 2^n*3*x^2 + 3^n*6*x^3 + 4^n*10*x^4 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, k^m*k*(k+1)/2*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 05 2009
STATUS
approved