A224797 E.g.f. satisfies: A(x) = Sum_{n>=0} (exp(x*A(x)^n) - 1)^n / n!.

1, 1, 4, 35, 503, 10207, 268865, 8731102, 337630732, 15165277773, 776576049655, 44683002944571, 2855602714004089, 200794017101260026, 15413426272667102594, 1283152929854467388195, 115198576226248396583523, 11099504126776462035978911

Offset: 0

Author

Paul D. Hanna, Apr 18 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 503*x^4/4! + 10207*x^5/5! +...
where
A(x) = 1 + (exp(x*A(x)) - 1) + (exp(x*A(x)^2) - 1)^2/2! + (exp(x*A(x)^3) - 1)^3/3! + (exp(x*A(x)^4) - 1)^4/4! + (exp(x*A(x)^5) - 1)^5/5! +...
		

Crossrefs

Cf. A189981.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, (exp(x*A^m +x*O(x^n))-1)^m/m!)); n!*polcoeff(A, n)}
for(n=0,21,print1(a(n),", "))

PARI

{Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling2(m, k)*(A+x*O(x^n))^(m*k))*x^m/m!)); n!*polcoeff(A, n)}
for(n=0,21,print1(a(n),", "))

Formula

E.g.f. satisfies: A(x) = Sum_{n>=0} Sum_{k=0..n} Stirling2(n, k)*A(x)^(n*k) * x^n/n!.