A217251 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * exp(n*x*A(n*x)) / n!.

1, 1, 3, 16, 149, 2196, 47887, 1503874, 66909705, 4169455768, 362532436091, 43987829285214, 7442339208497437, 1752526591489955620, 573506919224762378871, 260490696017559308642506, 163929335780245427253134993, 142635351437113204426676060976, 171300311626537525852633862663155

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..18.

Example

 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 149*x^4/4! + 2196*x^5/5! +...
where
A(x) = 1 + x*exp(x*A(x)) + x^2*exp(2*x*A(2*x))/2! + x^3*exp(3*x*A(3*x))/3! + x^4*exp(4*x*A(4*x))/4! +...

Prog

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

Crossrefs

Cf. A214933, A000272.

Sequence in context: A368451 A214933 A230323 * A125281 A086371 A229954

Adjacent sequences: A217248 A217249 A217250 * A217252 A217253 A217254

Keyword

nonn

Author

Paul D. Hanna, Mar 16 2013

Status

approved