A120012 The third self-composition of A120009; g.f.: A(x) = G(G(G(x))), where G(x) = g.f. of A120009.

1, 3, 9, 24, 42, -87, -1575, -12240, -77730, -449994, -2470278, -13101228, -67823484, -344888619, -1729791975, -8581375224, -42194252106, -205940062998, -998899022898, -4819339232640, -23144643733428, -110703908388582, -527633003316726, -2506857120078336

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Formula

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).

Example

A(x) = x + 3*x^2 + 9*x^3 + 24*x^4 + 42*x^5 - 87*x^6 - 1575*x^7 +...
G(x) = x + x^2 + x^3 - 6*x^5 - 33*x^6 - 143*x^7 - 572*x^8 +...
where G(x) is the g.f. of A120009 and G(G(G(x))) = A(x).

Prog

(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)}

Crossrefs

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

Sequence in context: A254010 A338124 A024314 * A352640 A029530 A301740

Adjacent sequences: A120009 A120010 A120011 * A120013 A120014 A120015

Keyword

sign

Author

Paul D. Hanna, Jun 07 2006

Status

approved