A168450 G.f. A(x) satisfies: A(x) = G(x*A(x)) where A(x/G(x)) = G(x) = g.f. of A004304, where A004304(n) is the number of planar tree-rooted maps with n edges.

1, 2, 6, 26, 148, 1012, 7824, 65886, 590452, 5546972, 54070432, 542937320, 5586265280, 58659600352, 626702981084, 6795682231830, 74645847739012, 829257675740724, 9304974123394272, 105343378754088424

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..850

Formula

G.f.: A(x) = F(x/A(x)) where A(x*F(x)) = F(x) = g.f. of A005568, where A005568(n) is the product of two successive Catalan numbers C(n)*C(n+1).

G.f.: A(x) = x/Series_Reversion(x*F(x)) where F(x) = g.f. of A005568.

G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where G(x) = g.f. of A004304.

Example

G.f. A(x) = 1 + 2*x + 6*x^2 + 26*x^3 + 148*x^4 + 1012*x^5 + 7824*x^6 +...
A(x) satisfies: A(x*F(x)) = F(x) = g.f. of A005568:
F(x) = 1 + 2*x + 10*x^2 + 70*x^3 + 588*x^4 + 5544*x^5 + 56628*x^6 +...+ A000108(n)*A000108(n+1)*x^n +...
A(x) satisfies: A(x/G(x)) = G(x) = g.f. of A004304:
G(x) = 1 + 2*x + 2*x^2 + 6*x^3 + 28*x^4 + 160*x^5 + 1036*x^6 +...

Prog

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

Crossrefs

Cf. A004304, A005568, A000108, variant: A168344.

Sequence in context: A178324 A002710 A132609 * A125224 A052844 A375629

Adjacent sequences: A168447 A168448 A168449 * A168451 A168452 A168453

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2009

Status

approved