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%I #9 Jan 25 2025 12:47:10
%S 1,1,4,25,200,1948,23293,366698,8669713,354287410,26296911212,
%T 3452678049185,778932197922145,297680194679224221,
%U 192063113715788790619,208413189299565620902495,381159431868835826320370849,1171978295935406653806412222411
%N G.f.: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(3^n).
%e G.f.: A(x) = 1 + x + 4*x^2 + 25*x^3 + 200*x^4 + 1948*x^5 + 23293*x^6 +...
%e where
%e A(x) = 1 + x*A(x)^3 + x^2*A(x)^9 + x^3*A(x)^27 + x^4*A(x)^81 +...
%e Related expansions begin:
%e A(x)^3 = 1 + 3*x + 15*x^2 + 100*x^3 + 810*x^4 + 7767*x^5 + 89506*x^6 +...
%e A(x)^9 = 1 + 9*x + 72*x^2 + 597*x^3 + 5310*x^4 + 51606*x^5 + 563469*x^6 +...
%e A(x)^27 = 1 + 27*x + 459*x^2 + 6408*x^3 + 81216*x^4 + 984501*x^5 + 11824992*x^6 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(3^j))); polcoeff(A, n)}
%Y Cf. A195259, A107589, A159609.
%K nonn,changed
%O 0,3
%A _Paul D. Hanna_, Sep 13 2011