%I #3 May 16 2018 16:53:44
%S 1,0,1,4,45,646,11791,256384,6423769,181427754,5689282946,
%T 195908618092,7345423236232,297860411541226,12990182010207113,
%U 606403416131651092,30175914326945883879,1594887978524453295830,89239745135865040868793,5270747814747645030300220,327731421167826049968117819,21401517667824383352272329174
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^(n-1) - A(x)^n )^n.
%e G.f.: A(x) = 1 + x^2 + 4*x^3 + 45*x^4 + 646*x^5 + 11791*x^6 + 256384*x^7 + 6423769*x^8 + 181427754*x^9 + 5689282946*x^10 + 195908618092*x^11 + ...
%e such that
%e 1 = 1 + (1 - A(x)) + ((1+x) - A(x)^2)^2 + ((1+x)^2 - A(x)^3)^3 + ((1+x)^3 - A(x)^4)^4 + ((1+x)^4 - A(x)^5)^5 + ((1+x)^5 - A(x)^6)^6 + ((1+x)^6 - A(x)^7)^7 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ((1+x)^(m-1) - Ser(A)^m)^m ) )[#A] ); A[n+1]}
%o for(n=0, 30, print1(a(n), ", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, May 16 2018