A120012 - OEIS

%I #8 Mar 11 2015 04:13:57

%S 1,3,9,24,42,-87,-1575,-12240,-77730,-449994,-2470278,-13101228,

%T -67823484,-344888619,-1729791975,-8581375224,-42194252106,

%U -205940062998,-998899022898,-4819339232640,-23144643733428,-110703908388582,-527633003316726,-2506857120078336

%N The third self-composition of A120009; g.f.: A(x) = G(G(G(x))), where G(x) = g.f. of A120009.

%F G.f.: A(x) = x*(7 - 36*x - 3*(1-5*x)*C(x) )/(2-9*x)^2 where C(x) = (1-sqrt(1-4*x))/(2*x) is the Catalan function (A000108).

%e A(x) = x + 3*x^2 + 9*x^3 + 24*x^4 + 42*x^5 - 87*x^6 - 1575*x^7 +...

%e G(x) = x + x^2 + x^3 - 6*x^5 - 33*x^6 - 143*x^7 - 572*x^8 +...

%e where G(x) is the g.f. of A120009 and G(G(G(x))) = A(x).

%o (PARI) {a(n)=local(k=3,x=X+X^3*O(X^n));polcoeff( x*((1-k+k^2)-k^2*(k+1)*x-k*(1-(k+2)*x)*(1-sqrt(1-4*x))/2/x)/(1-k+k^2*x)^2,n,X)}

%Y Cf. A120009, A127275 (2nd self-composition); A000108 (Catalan).

%K sign

%O 1,2

%A _Paul D. Hanna_, Jun 07 2006