A046647 Number of certain rooted planar maps.

1, 6, 26, 120, 594, 3094, 16728, 93024, 528770, 3058770, 17948970, 106585440, 639318456, 3867821640, 23574446992, 144621823632, 892293152994, 5533289372170, 34468829508750, 215594574231960, 1353464311979010, 8525237988890070, 53862849664172640, 341258716548422400

Offset

2,2

Links

Table of n, a(n) for n=2..25.

William G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.

William G. Brown, Enumeration of non-separable planar maps [Annotated scanned copy]

Formula

a(2) = 1; a(n) = 4*(7*n-15)*(3*n-6)!/((n-2)!*(2n-2)!). - Emeric Deutsch, Mar 03 2004

G.f.: (g+1)*(3*g+1)/(g-1)^2 where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

a(n) ~ 7 * 3^(3*n-11/2) / (2^(2*n-3) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 19 2025

Mathematica

a[n_] := 4 * (7*n-15) * (3*n-6)! / ((n-2)!*(2n-2)!); a[2] = 1; Array[a, 20, 2] (* Amiram Eldar, Sep 19 2025 *)

Crossrefs

A diagonal of A046651.

Cf. A046646.

Sequence in context: A287806 A164549 A283341 * A233075 A307331 A298625

Adjacent sequences: A046644 A046645 A046646 * A046648 A046649 A046650

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 03 2004

More terms from Amiram Eldar, Sep 19 2025

Status

approved