A168357 Self-convolution of A006664, which is the number of irreducible systems of meanders.

1, 2, 5, 20, 112, 768, 5984, 50856, 460180, 4366076, 42988488, 436066232, 4532973676, 48095557700, 519247705968, 5690272928520, 63172884082028, 709373555125356, 8046263496489260, 92089662771965492, 1062482514810065752

Offset: 0

Author

Paul D. Hanna, Nov 23 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 112*x^4 + 768*x^5 +...
A(x)^(1/2) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 322*x^5 + 2546*x^6 +...+ A006664(n)*x^n +...
G.f. satisfies: A(x*F(x)^2) = F(x)^2 where 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 +...
F(x)^2 = 1 + 2*x + 9*x^2 + 58*x^3 + 458*x^4 + 4120*x^5 + 40569*x^6 +...+ A168358(n)*x^n +...
		

Crossrefs

Cf. A168358, A168344, A001246, A006664, A000108.

Programs

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)^2), n)}

Formula

G.f.: A(x) = x/Series_Reversion(x*F(x)^2) where F(x) = g.f. of A001246, which is the squares of Catalan numbers.

G.f.: A(x) = F(x/A(x))^2 where A(x*F(x)^2) = F(x)^2 where F(x) = g.f. of A001246.