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%I #6 Aug 11 2021 13:58:18
%S 1,1,4,31,362,5567,104229,2268586,55817457,1524956611,45699911560,
%T 1489007130546,52390324106713,1979726546053502,79978929224189504,
%U 3440756672193895992,157085559415640319126,7587124626671398460006,386598739562989187413005,20728976430148069600767400,1166849728839227202686314988
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (n - A(x)^n)^n.
%H Paul D. Hanna, <a href="/A322626/b322626.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ c * n^(n+1), where c = 0.6410371541108... - _Vaclav Kotesovec_, Aug 11 2021
%e G.f.: A(x) = 1 + x + 4*x^2 + 31*x^3 + 362*x^4 + 5567*x^5 + 104229*x^6 + 2268586*x^7 + 55817457*x^8 + 1524956611*x^9 + 45699911560*x^10 + ...
%e such that
%e 1 = 1 + x*(1 - A(x)) + x^2*(2 - A(x)^2)^2 + x^3*(3 - A(x)^3)^3 + x^4*(4 - A(x)^4)^4 + x^5*(5 - A(x)^5)^5 + x^6*(6 - A(x)^6)^6 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = Vec(sum(m=0,#A, x^m*(m - Ser(A)^m)^m))[#A+1]); A[n+1]}
%o for(n=0,25,print1(a(n),", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 28 2019