A213905 - OEIS

%I #7 Aug 20 2017 16:23:09

%S 1,1,1,2,4,9,20,47,112,274,678,1702,4314,11039,28460,73875,192884,

%T 506251,1334899,3534591,9394196,25052866,67019457,179793858,483591479,

%U 1303836901,3523141231,9539570474,25879559378,70332798052,191461351903,522012186777,1425327940690

%N G.f. satisfies: A(x) = x^2+x^3 + A(A(x)).

%H Paul D. Hanna, <a href="/A213905/b213905.txt">Table of n, a(n) for n = 2..301</a>

%e G.f.: A(x) = x^2 + x^3 + x^4 + 2*x^5 + 4*x^6 + 9*x^7 + 20*x^8 + 47*x^9 +...

%e where

%e A(A(x)) = x^4 + 2*x^5 + 4*x^6 + 9*x^7 + 20*x^8 + 47*x^9 + 112*x^10 +...

%o (PARI) {a(n)=local(A=x^2+x^3); for(i=1,n, A = x^2 + x^3 + subst(A,x,A+x*O(x^n))); polcoeff(A,n)}

%o for(n=2,40,print1(a(n),", "))

%Y Cf. A213906.

%K nonn

%O 2,4

%A _Paul D. Hanna_, Jun 24 2012