login
G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (n - A(x)^n)^n.
1

%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