A218682 E.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n/n! * A(n*x)^n.

1, 1, 6, 93, 2944, 167685, 16037376, 2481455137, 609371157312, 235171042752105, 141778378915235200, 132871933962627534741, 192678752056300896500544, 430404642833695770472870573, 1474859949355240010986735351872, 7723091241704594423130951106689225

Offset: 0

Author

Paul D. Hanna, Nov 05 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 6*x^2/2! + 93*x^3/3! + 2944*x^4/4! + 167685*x^5/5! +...
where
A(x) = 1 + x*A(x) + 2^2*x^2*A(2*x)^2/2! + 3^3*x^3*A(3*x)^3/3! + 4^4*x^4*A(4*x)^4/4! +...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..55

Crossrefs

Cf. A192036, A218683.

Programs

Mathematica

m = 16; A[_] = 0;
Do[A[x_] = Sum[If[n == 0, 1, n^n x^n/n! A[n x]^n], {n, 0, m}] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] * Range[0, m - 1]! (* Jean-François Alcover, Oct 03 2019 *)

PARI

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