A191809 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+2,3).

1, 1, 2, 7, 32, 174, 1071, 7281, 53943, 432555, 3743146, 34934853, 351853883, 3827477399, 44985837602, 570985992828, 7814212692498, 115024461077654, 1815588345261996, 30628743324667923, 550414603283527315, 10503650627005928698

Offset: 0

Author

Paul D. Hanna, Jun 16 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 32*x^4 + 174*x^5 + 1071*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^4 + x^3*A(x)^10 + x^4*A(x)^20 + x^5*A(x)^35 + x^6*A(x)^56 + x^7*A(x)^84 +...+ x^n*A(x)^(n*(n+1)*(n+2)/3!) +...
		

Crossrefs

Cf. A107591, A191810, A191811, A191812.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(m*(m+1)*(m+2)/3!)));polcoeff(A,n)}