A221101 E.g.f. satisfies: A(x) = Sum_{n>=0} log(1 + x*A(n*x))^n/n!.

1, 1, 2, 12, 144, 3160, 118380, 7174188, 692356896, 104696597808, 24680489921280, 9010186432576560, 5073501307520289600, 4385657278007399474496, 5797249519065509217375936, 11674185903250032386477342880, 35692663320428574506107140979200

Offset: 0

Author

Paul D. Hanna, Jan 01 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 144*x^4/4! + 3160*x^5/5! +...
where
A(x) = 1 + log(1 + x*A(x)) + log(1 + x*A(2*x))^2/2! + log(1 + x*A(3*x))^3/3! + log(1 + x*A(4*x))^4/4! +...
		

Crossrefs

Cf. A189981, A221100.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, log(1+x*subst(A,x,m*x+x*O(x^n)))^m/m!)); n!*polcoeff(A, n)}
for(n=0,20,print1(a(n),", "))

PARI

{Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling1(m, k)*subst(A,x,k*x+x*O(x^n))^m)*x^m/m!)); n!*polcoeff(A, n)}
for(n=0,20,print1(a(n),", "))

Formula

E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling1(n,k) * A(k*x)^n/n!.