G.f. A(x) satisfies: A(x) = G(x*A(x)) where A(x/G(x)) = G(x) = g.f. of A006664, which is the number of irreducible systems of meanders.

1, 1, 3, 15, 99, 773, 6743, 63591, 635307, 6634599, 71759983, 798563065, 9098321475, 105733563393, 1249676348391, 14986826364311, 182027688352427, 2235713532561779, 27732857308708571, 347064951865766607

0,3

G.f.: A(x) = F(x/A(x)) where A(x*F(x)) = F(x) = g.f. of A001246, which is the squares of Catalan numbers.

G.f.: A(x) = x/Series_Reversion(x*F(x)) where F(x) = g.f. of A001246.

G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where G(x) = g.f. of A006664.

G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 99*x^4 + 773*x^5 + 6743*x^6 +...

A(x) satisfies: A(x*F(x)) = F(x) = g.f. of A001246:

F(x) = 1 + x + 4*x^2 + 25*x^3 + 196*x^4 + 1764*x^5 + 17424*x^6 +...+ A000108(n)^2*x^n +...

A(x) satisfies: A(x/G(x)) = G(x) = g.f. of A006664:

G(x) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 322*x^5 + 2546*x^6 +...

(PARI) {a(n)=local(C_2=vector(n+1, m, (binomial(2*m-2, m-1)/m)^2)); polcoeff(x/serreverse(x*Ser(C_2)), n)}

Cf. A006664, A001246, A000108.

Cf. A168450 (variant). [From Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2009]

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 23 2009

Typo in formula corrected by Paul D. Hanna (pauldhanna(AT)juno.com), Nov 24 2009

approved