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 A154835 G.f. satisfies: A(x) = x + A((x+x^2)*A(x)) with A(0)=0. 0

%I #2 Mar 30 2012 18:37:15

%S 1,1,2,4,10,26,72,205,597,1770,5329,16253,50112,155939,489111,1544723,

%T 4908164,15678715,50323541,162213311,524895810,1704407999,5552027379,

%U 18137964251,59412854411,195090277189,642056206297,2117485840188

%N G.f. satisfies: A(x) = x + A((x+x^2)*A(x)) with A(0)=0.

%e G.f.: A(x) = x + x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...

%e A((x+x^2)*A(x)) = x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...

%e Let G(x) = (x+x^2)*A(x) then

%e A(x) = x + G(x) + G(G(x)) + G(G(G(x))) + G(G(G(G(x)))) + ... where

%e G(x) = x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 14*x^6 + 36*x^7 + 98*x^8 +...;

%e G(G(x)) = x^4 + 4*x^5 + 12*x^6 + 36*x^7 + 106*x^8 + 312*x^9 +...;

%e G(G(G(x))) = x^8 + 8*x^9 + 40*x^10 + 168*x^11 + 646*x^12 +...;

%e G(G(G(G(x)))) = x^16 + 16*x^17 + 144*x^18 + 976*x^19 +...; ...

%o (PARI) {a(n)=local(A=x+x*O(x));for(i=0,n,A=x+subst(A,x,x*(1+x)*A));polcoeff(A,n)}

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jan 16 2009

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Last modified August 6 14:07 EDT 2024. Contains 374974 sequences. (Running on oeis4.)