A161971 E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x) ) ), where A'(x) = d/dx A(x).

1, 1, 3, 28, 521, 15596, 672457, 39049396, 2919995969, 272314100944, 30921124212881, 4195725816103724, 670156359448985521, 124435720115244671056, 26578720273153614206201

Offset: 0

Author

Paul D. Hanna, Jun 23 2009

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 521*x^4/4! + 15596*x^5/5! +...
exp(x*A'(x)) = 1 + x + 7*x^2/2! + 103*x^3/3! + 2565*x^4/4! + 94881*x^5/5! +...
where log(A(x)) = x*exp(x*A'(x)):
log(A(x)) = x + 2*x^2/2! + 21*x^3/3! + 412*x^4/4! + 12825*x^5/5! + 569286*x^6/6! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..230

Crossrefs

Cf. A161967 (variant).

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(x*exp(x*deriv(A)+O(x^n))));n!*polcoeff(A,n)}

Formula

a(n) ~ c * n * (n!)^2, where c = 0.2773256592699... - Vaclav Kotesovec, Aug 24 2017