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A120899 G.f. satisfies: A(x) = C(x)^2 * A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108). 7
1, 2, 5, 16, 54, 186, 654, 2338, 8463, 30938, 114022, 423096, 1579049, 5922512, 22309350, 84354388, 320020227, 1217689680, 4645693038, 17766596202, 68092473570, 261486788434, 1005962436536, 3876412305114, 14960183283203 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Column 0 of triangle A120898 (cascadence of 1+2x+x^2). Self-convolution of A120900.

LINKS

Table of n, a(n) for n=0..24.

EXAMPLE

A(x) = 1 + 2*x + 5*x^2 + 16*x^3 + 54*x^4 + 186*x^5 + 654*x^6 +...

= C(x)^2 * 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^2*subst(A, x, x^3*C^4 +x*O(x^n))); polcoeff(A, n, x)}

CROSSREFS

Cf. A120898, A120900 (square-root), A120901, A120902; A000108; variants: A092684, A092687, A120895.

Sequence in context: A006191 A149959 A161941 * A149960 A149961 A141754

Adjacent sequences:  A120896 A120897 A120898 * A120900 A120901 A120902

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 14 2006

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)