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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). 0
1, 1, 3, 6, 20, 70, 302, 1386, 6902, 35862, 194202, 1082642, 6191680, 36141118, 214715244, 1294849186, 7911159522, 48888093910, 305165808290, 1921992409066, 12202404037088, 78031629139246, 502263432618224, 3252160882871210 (list; graph; refs; listen; history; text; internal format)
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 A162171 A194992

Adjacent sequences:  A168591 A168592 A168593 * A168595 A168596 A168597

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 01 2009

STATUS

approved

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)