A120017 - OEIS

%I #8 Mar 10 2015 02:16:54

%S 1,2,4,10,32,116,440,1708,6760,27232,111392,461536,1933024,8170400,

%T 34807232,149304080,644298592,2795216576,12184415360,53338632256,

%U 234393350912,1033614750080,4572427361536,20285780245120,90238113332992

%N The 2nd self-composition of A120010; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A120010.

%F G.f.: A(x) = (1 - sqrt(1 - 4*x*(1-x)/(1-2*x+2*x^2) ))/2.

%e A(x) = x + 2*x^2 + 4*x^3 + 10*x^4 + 32*x^5 + 116*x^6 + 440*x^7 +...

%e G(x) = x + x^2 + x^3 + 2*x^4 + 6*x^5 + 18*x^6 + 53*x^7 + 158*x^8 +...

%e where G(x) is the g.f. of A120010 and G(G(x)) = A(x).

%o (PARI) {a(n)=polcoeff((1 - sqrt(1 - 4*x*(1-x)/(1-2*x+2*x^2+x*O(x^n)) ))/2, n)}

%Y Cf. A120010, A120018 (3rd self-composition).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 14 2006