A214933 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * exp(n*x*A(x)^n) / n!.

1, 1, 3, 16, 149, 1956, 33487, 710914, 18051945, 534541240, 18111042971, 691843182174, 29448194808397, 1383323874167860, 71145082349453127, 3979392388532436586, 240697239447634403153, 15667133474066968379376, 1092794908568878699158835, 81380508121010249600574646

Offset

0,3

Comments

Compare to: W(x) = Sum_{n>=0} x^n * exp(n*x*W(x)) / n! where W(x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.

Links

Table of n, a(n) for n=0..19.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 149*x^4/4! + 1956*x^5/5! +...
where
A(x) = 1 + x*exp(x*A(x)) + x^2*exp(2*x*A(x)^2)/2! + x^3*exp(3*x*A(x)^3)/3! + x^4*exp(4*x*A(x)^4)/4! +...

Prog

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

Crossrefs

Cf. A217251, A000272.

Sequence in context: A264660 A362655 A368451 * A230323 A217251 A125281

Adjacent sequences: A214930 A214931 A214932 * A214934 A214935 A214936

Keyword

nonn

Author

Paul D. Hanna, Mar 09 2013

Status

approved