A073773 Number of plane binary trees of size n+2 and height n.

0, 0, 0, 6, 40, 152, 480, 1376, 3712, 9600, 24064, 58880, 141312, 333824, 778240, 1794048, 4096000, 9273344, 20840448, 46530560, 103284736, 228065280, 501219328, 1096810496, 2390753280, 5192548352, 11240734720, 24259854336

Offset: 0

Author

Antti Karttunen, Aug 11 2002

Keywords

• nonn

Examples

			a(3) = 6 because there exists only these six binary trees of size 5 and height 3:
_\/\/_______\/\/_\/_\/_____\/_\/_\/___\/___V_V___
__\/_\/___\/_\/___\/_\/___\/_\/___\/_\/___\/_\/__
___\./_____\./_____\./_____\./_____\./_____\./___
		

Links

• Henry Bottomley & Antti Karttunen Derivations of the formulas for the diagonals of A073345 & A073346.

Crossrefs

Cf. A014480, A073345, A073774, A028878.

Programs

Maple

A073773 := n -> `if`((n < 3),0,((n^2 - 6)*2^(n-2)));

Formula

a(n) = A073345(n+2, n).

a(n < 3) = 0, a(n) = ((n^2 - 6)*2^(n-2)).