A218682 - OEIS

%I #8 Oct 03 2019 04:21:33

%S 1,1,6,93,2944,167685,16037376,2481455137,609371157312,

%T 235171042752105,141778378915235200,132871933962627534741,

%U 192678752056300896500544,430404642833695770472870573,1474859949355240010986735351872,7723091241704594423130951106689225

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

%H Alois P. Heinz, <a href="/A218682/b218682.txt">Table of n, a(n) for n = 0..55</a>

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

%e where

%e 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! +...

%t m = 16; A[_] = 0;

%t 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}];

%t CoefficientList[A[x], x] * Range[0, m - 1]! (* _Jean-François Alcover_, Oct 03 2019 *)

%o (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)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A192036, A218683.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 05 2012