OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = B(x*A(x)) and A(x/B(x)) = B(x) where B(x) satisfies:
B(x) = Sum_{n>=0} n!*x^n * B(x)^(n*(n-1)/2) and is the g.f. of A219358.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 99*x^4 + 785*x^5 + 7151*x^6 +...
where
A(x) = 1 + 1!*x*A(x) + 2!*x^2*A(x)^3 + 3!*x^3*A(x)^6 + 4!*x^4*A(x)^10 + 5!*x^5*A(x)^15 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, k!*x^k*(A+x*O(x^n))^(k*(k+1)/2))); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 18 2012
STATUS
approved