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%I #4 Mar 19 2019 20:29:28
%S 1,1,1,2,3,9,21,76,241,962,3687,15930,68993,320025,1511977,7471685,
%T 37780922,197506241,1056928087,5810534182,32667061545,187952045908,
%U 1104355482420,6623724997302,40514607315969,252490521215350,1602602016169781,10349126940718990,67984993381548943,453846136553840921,3078734565764856380,21202631838742029002,148238158399524358952,1051257411796217414475
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (1 + n*x)^n / A(x)^(n+1).
%H Paul D. Hanna, <a href="/A324614/b324614.txt">Table of n, a(n) for n = 0..300</a>
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 9*x^5 + 21*x^6 + 76*x^7 + 241*x^8 + 962*x^9 + 3687*x^10 + 15930*x^11 + 68993*x^12 + 320025*x^13 + 1511977*x^14 + ...
%e such that
%e 1 = 1/A(x) + x*(1+x)/A(x)^2 + x^2*(1+2*x)^2/A(x)^3 + x^3*(1+3*x)^3/A(x)^4 + x^4*(1+4*x)^4/A(x)^5 + x^5*(1+5*x)^5/A(x)^6 + x^6*(1+6*x)^6/A(x)^7 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
%o A[#A] = polcoeff( sum(n=0,#A, x^n*(1+n*x)^n/Ser(A)^(n+1)), #A-1););A[n+1]}
%o for(n=0,40, print1(a(n),", "))
%Y Cf. A303058.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Mar 19 2019
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