|
Search: id:A120895
|
|
|
| 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). |
|
+0
7
|
|
| 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; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Equals column 0 and main diagonal of triangle A120894 (cascadence of 1+x+x^2).
|
|
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.
|
|
PROGRAM
|
(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 this_sequence A101785 A003089 A112412
Adjacent sequences: A120892 A120893 A120894 this_sequence A120896 A120897 A120898
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 14 2006
|
|
|
Search completed in 0.002 seconds
|
