A231868 E.g.f. satisfies: A'(x) = A(x*A(x)) with A(0)=1.

1, 1, 1, 3, 12, 84, 774, 9468, 146052, 2764980, 62759736, 1678881096, 52185496464, 1862666455104, 75581146734912, 3456542059903296, 176834245093202736, 10053690187338014256, 631507398302281340736, 43596564604477924096512, 3292312674449093132923488

Offset: 0

Author

Paul D. Hanna, Nov 14 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + x^2/2! + 3*x^3/3! + 12*x^4/4! + 84*x^5/5! + 774*x^6/6! + ...
such that
A(x*A(x)) = A'(x) = 1 + x + 3*x^2/2! + 12*x^3/3! + 84*x^4/4! + 774*x^5/5! + ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..175

Crossrefs

Cf. A001028, A231619.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+intformal(subst(A,x,x*A +x*O(x^n))));n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))

Formula

E.g.f. satisfies: A(x) = 1 + Integral( A(x*A(x)) dx).