

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).


3



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
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OFFSET

0,3


COMMENTS

Selfconvolution 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



