A219358 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * A(x)^(n*(n-1)/2).

1, 1, 2, 8, 46, 334, 2882, 28604, 320248, 3993184, 54942740, 828086732, 13586200504, 241294019584, 4615319816192, 94629675177320, 2070911506927360, 48185049542009248, 1187816429730925424, 30923773410431125424, 847808674826433774928, 24414218135569507213312

Offset: 0

Author

Paul D. Hanna, Nov 18 2012

Keywords

• nonn
• changed

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 334*x^5 + 2882*x^6 +...
where
A(x) = 1 + 1!*x + 2!*x^2*A(x) + 3!*x^3*A(x)^3 + 4!*x^4*A(x)^6 + 5!*x^5*A(x)^10 + 6!*x^6*A(x)^15 +...
		

Crossrefs

Cf. A155804, A219359.

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 A219359.