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A195259 G.f.: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(3^(n-1)). 1

%I

%S 1,1,2,6,25,138,1036,11270,194105,5600367,275058868,22805688464,

%T 3173290832407,739292604671606,288039050041591288,

%U 188101949731185856592,205677982188934721693289,377993929252274297946197815,1165828413037318706712871579130

%N G.f.: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(3^(n-1)).

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 138*x^5 + 1036*x^6 +...

%e where

%e A(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^9 + x^4*A(x)^27 + x^5*A(x)^81 +...

%e Related expansions begin:

%e A(x)^3 = 1 + 3*x + 9*x^2 + 31*x^3 + 129*x^4 + 666*x^5 + 4499*x^6 +...

%e A(x)^9 = 1 + 9*x + 54*x^2 + 282*x^3 + 1431*x^4 + 7560*x^5 + 44568*x^6 +...

%e A(x)^27 = 1 + 27*x + 405*x^2 + 4491*x^3 + 41391*x^4 + 338580*x^5 + 2571669*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-1)))); polcoeff(A, n)}

%Y Cf. A195260, A107589, A159609.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 13 2011

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Last modified August 8 21:55 EDT 2022. Contains 356016 sequences. (Running on oeis4.)