A168451 Self-convolution of A004304, where A004304(n) is the number of planar tree-rooted maps with n edges.

1, 4, 8, 20, 84, 456, 2860, 19708, 145120, 1122680, 9023784, 74777248, 635292016, 5510485600, 48644137764, 435920025116, 3957758805776, 36345636909032, 337159090063880, 3155827384249824, 29776934546342464, 283001546964599248

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..840

Formula

G.f.: A(x) = x/Series_Reversion(x*F(x)^2) where 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) = F(x/A(x))^2 where A(x*F(x)^2) = F(x)^2 where F(x) = g.f. of A005568.

Example

G.f.: A(x) = 1 + 4*x + 8*x^2 + 20*x^3 + 84*x^4 + 456*x^5 + 2860*x^6 +...
A(x)^(1/2) = 1 + 2*x + 2*x^2 + 6*x^3 + 28*x^4 + 160*x^5 + 1036*x^6 +...+ A004304(n)*x^n +...
G.f. satisfies: A(x*F(x)^2) = F(x)^2 where 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 +...
F(x)^2 = 1 + 4*x + 24*x^2 + 180*x^3 + 1556*x^4 + 14840*x^5 + 152092*x^6 +...+ A168452(n)*x^n +...

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)^2)), n)}

Crossrefs

Cf. A168452, A004304, A005568, A000108, variant: A168357.

Sequence in context: A187010 A240149 A086912 * A000585 A209451 A102559

Adjacent sequences: A168448 A168449 A168450 * A168452 A168453 A168454

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2009

Status

approved