OFFSET
0,2
FORMULA
a(n) = Sum_{k=1..n} k*(k+3)/2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.
EXAMPLE
E.g.f: A(x) = 1 + 2*x + 14*x^2/2! + 194*x^3/3! + 4280*x^4/4! + 134232*x^5/5! +...
log(A(x)) = 2*1*x + 5*2*x^2/2! + 9*14*x^3/3! + 14*194*x^4/4! + 20*4280*x^5/5! +...
PROG
(PARI) {a(n)=if(n==0, 1, n!*polcoeff(exp(sum(k=1, n, k*(k+3)/2*a(k-1)*x^k/k!)+x*O(x^n)), n))}
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, k*(k+3)/2*binomial(n-1, k-1)*a(k-1)*a(n-k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 08 2009
STATUS
approved