A219359 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n+1)/2).

1, 1, 3, 15, 99, 785, 7151, 73097, 827501, 10295549, 140100323, 2077648871, 33466994639, 583535328293, 10971899911703, 221571516903233, 4786126571515961, 110142864494603313, 2690257065904106571, 69500954207702580927, 1893141166438848208747, 54217997416999007587201

Offset: 0

Author

Paul D. Hanna, Nov 18 2012

Keywords

• nonn
• changed

Examples

			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 +...
		

Crossrefs

Cf. A155805, A107591, A219358.

Programs

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), ", "))

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.