A168594 G.f. A(x) satisfies: A(x) = F(x/A(x)) where A(x*F(x)) = F(x) = g.f. of A133053, which is the squares of Motzkin numbers (A001006).

1, 1, 3, 6, 20, 70, 302, 1386, 6902, 35862, 194202, 1082642, 6191680, 36141118, 214715244, 1294849186, 7911159522, 48888093910, 305165808290, 1921992409066, 12202404037088, 78031629139246, 502263432618224, 3252160882871210

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: A(x) = x/Series_Reversion(x*F(x)) where F(x) = g.f. of A133053.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 20*x^4 + 70*x^5 + 302*x^6 +...
A(x) satisfies: A(x*F(x)) = F(x) = g.f. of A133053:
F(x) = 1 + x + 4*x^2 + 16*x^3 + 81*x^4 + 441*x^5 + 2601*x^6 +...+ A001006(n)^2*x^n +...

Prog

(PARI) {a(n)=if(n==0, 1, polcoeff(x/serreverse(x*sum(m=0, n, polcoeff((1/x)*serreverse(x/(1+x+x^2+x^2*O(x^m))), m)^2 *x^m)+x^2*O(x^n)), n))}

Crossrefs

Cf. A001006, A133053, A168344 (variant).

Sequence in context: A173110 A090371 A288817 * A123559 A334329 A162171

Adjacent sequences: A168591 A168592 A168593 * A168595 A168596 A168597

Keyword

nonn

Author

Paul D. Hanna, Dec 01 2009

Status

approved