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Search: id:A121399
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| A121399 |
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G.f. satisfies: A(x) = G(x)*A(x^2*G(x)) where G(x) is the g.f. of the Motzkin numbers (A001006): G = (1 + x*G + x^2*G^2). |
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+0
3
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| 1, 1, 3, 6, 17, 42, 114, 302, 827, 2263, 6275, 17468, 48967, 137834, 389738, 1105861, 3148240, 8987989, 25726635, 73808069, 212196040, 611219900, 1763659860, 5097131364, 14752847173, 42757853357, 124080269331, 360493591232
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals column 0 of triangle A121400.
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EXAMPLE
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A(x) = 1 + x + 3*x^2 + 6*x^3 + 17*x^4 + 42*x^5 + 114*x^6 +...
The g.f. of the Motzkin numbers begins:
G(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 21*x^5 + 51*x^6 + 127*x^7 +...
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PROGRAM
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(PARI) {a(n)=local(F=1+x+x^2, G=serreverse(x/(F+x^2*O(x^n)))/x, H=1+x, A); for(i=0, n, H=G*subst(H, x, x^2*G)+x^2*O(x^n)); A=(x*H-y*subst(H, x, x*y))/(x*subst(F, x, y)-y); polcoeff(polcoeff(A, n, x), 0, y)}
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CROSSREFS
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Cf. A121400 (triangle), A121398 (main diagonal), A001006 (Motzkin).
Sequence in context: A151503 A007718 A089264 this_sequence A129905 A143363 A006081
Adjacent sequences: A121396 A121397 A121398 this_sequence A121400 A121401 A121402
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2006
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