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A120895 G.f. satisfies: A(x) = G(x)*A(x^3*G(x)^2) where G(x) is the g.f. of the Motzkin numbers (A001006). 6
1, 1, 2, 5, 12, 30, 78, 206, 552, 1498, 4105, 11340, 31541, 88237, 248076, 700478, 1985397, 5646129, 16104378, 46056513, 132031176, 379315946, 1091890772, 3148736064, 9095091878, 26310816944, 76219704957, 221085782559 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals column 0 and main diagonal of triangle A120894 (cascadence of 1+x+x^2).

LINKS

Table of n, a(n) for n=0..27.

EXAMPLE

A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 30*x^5 + 78*x^6 + 206*x^7+...

= G(x)*A(x^3*G(x)^2) where

G(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 21*x^5 + 51*x^6 + 127*x^7 +...

is the g.f. of the Motzkin numbers (A001006) so that G(x) satisfies:

G(x) = 1 + x*G(x) + x^2*G(x)^2.

PROG

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

CROSSREFS

Cf. A120894, A120896, A120897; A001006; variants: A092684, A092687, A120899.

Sequence in context: A145267 A103287 A136704 * A101785 A003089 A213263

Adjacent sequences:  A120892 A120893 A120894 * A120896 A120897 A120898

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 14 2006

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)