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%I #6 May 14 2019 22:11:34
%S 1,1,2,5,16,55,211,858,3709,16799,79393,389476,1975794,10336925,
%T 55626033,307348959,1740424149,10087499430,59764588797,361575122501,
%U 2231594755060,14039189350213,89957652033096,586694050333245,3892099566201798,26248657606212596,179864639698235287,1251657405383723002,8841433832652547890,63367819640545183277,460621983117854333354,3394551331802426437715
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (1 + n*x - A(x))^(n+1), where A(0) = 0.
%e G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 16*x^5 + 55*x^6 + 211*x^7 + 858*x^8 + 3709*x^9 + 16799*x^10 + 79393*x^11 + 389476*x^12 + 1975794*x^13 + ...
%e such that
%e 1 = (1 - A(x)) + x*(1 + x - A(x))^2 + x^2*(1 + 2*x - A(x))^3 + x^3*(1 + 3*x - A(x))^4 + x^4*(1 + 4*x - A(x))^5 + x^5*(1 + 5*x - A(x))^6 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = polcoeff( sum(n=0,#A, x^n * ( (1 + n*x) - x*Ser(A) )^(n+1) ),#A) );A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%K nonn
%O 1,3
%A _Paul D. Hanna_, May 14 2019
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