A120017 The 2nd self-composition of A120010; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A120010.

1, 2, 4, 10, 32, 116, 440, 1708, 6760, 27232, 111392, 461536, 1933024, 8170400, 34807232, 149304080, 644298592, 2795216576, 12184415360, 53338632256, 234393350912, 1033614750080, 4572427361536, 20285780245120, 90238113332992

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

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

Example

A(x) = x + 2*x^2 + 4*x^3 + 10*x^4 + 32*x^5 + 116*x^6 + 440*x^7 +...
G(x) = x + x^2 + x^3 + 2*x^4 + 6*x^5 + 18*x^6 + 53*x^7 + 158*x^8 +...
where G(x) is the g.f. of A120010 and G(G(x)) = A(x).

Prog

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

Crossrefs

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

Sequence in context: A336614 A071954 A352279 * A000736 A263663 A176006

Adjacent sequences: A120014 A120015 A120016 * A120018 A120019 A120020

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2006

Status

approved