A120900 G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).

1, 1, 2, 6, 19, 62, 209, 722, 2539, 9054, 32654, 118876, 436171, 1611067, 5984943, 22344455, 83786875, 315397144, 1191324649, 4513742858, 17149228138, 65318912291, 249356597492, 953902701488, 3656057618727, 14037222220896

Offset

0,3

Comments

Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2).

Links

Table of n, a(n) for n=0..25.

Example

A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +...
= C(x) * A(x^3*C(x)^4) where
C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.

Prog

(PARI) {a(n)=local(A=1+x, C=(1/x*serreverse(x/(1+2*x+x^2+x*O(x^n))))^(1/2)); for(i=0, n, A=C*subst(A, x, x^3*C^4 +x*O(x^n))); polcoeff(A, n, x)}

Crossrefs

Cf. A120898, A120899, A000108.

Sequence in context: A071738 A026012 A191993 * A284216 A059712 A059713

Adjacent sequences: A120897 A120898 A120899 * A120901 A120902 A120903

Keyword

nonn

Author

Paul D. Hanna, Jul 14 2006

Status

approved