|
%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
|
