A196531 E.g.f. satisfies: A(x) = Sum_{n>=0} exp(A(x)^n - 1)*A(x)^n*x^n/n!.

1, 1, 5, 52, 853, 19291, 557719, 19657667, 817847321, 39236975668, 2132767035851, 129548751144077, 8696909403827077, 639445475893738749, 51105213341360790655, 4411321463887034379616, 409004744372281965629617, 40539225718259037965353203

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

E.g.f. satisfies: A(x) = G(x*A(x)) where G(x) = A(x/G(x)) is the e.g.f. of A195895; thus, A(x) = (1/x)*Series_Reversion(x/G(x)).

Example

E.g.f.: A(x) = 1 + x + 5*x^2/2! + 52*x^3/3! + 853*x^4/4! + 19291*x^5/5! +...
where
A(x) = 1 + exp(A(x)-1)*A(x)*x + exp(A(x)^2-1)*A(x)^2*x^2/2! + exp(A(x)^3-1)*A(x)^3*x^3/3! +...
Also, A(x) = G(x*A(x)) where G(x) = A(x/G(x)) = e.g.f. of A195895(n):
G(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 201*x^4/4! + 2996*x^5/5! + 57613*x^6/6! +...+ A195895(n)*x^n/n! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, exp(A^m-1+x*O(x^n))*A^m*x^m/m!)); n!*polcoeff(A, n)}
(PARI) /* Alternate e.g.f. (requires high precision): */
{a(n)=local(A=1+x); for(i=1, n, A=exp(-1)*sum(m=0, 2*n+10, exp(x*A^(m+1)+x*O(x^n))/m!)); round(n!*polcoeff(A, n))}

Crossrefs

Cf. A195895.

Sequence in context: A367165 A377324 A357346 * A108459 A223898 A210096

Adjacent sequences: A196528 A196529 A196530 * A196532 A196533 A196534

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2011

Status

approved