A073774 Number of plane binary trees of size n+3 and height n.

0, 0, 0, 4, 68, 376, 1440, 4736, 14272, 40576, 110592, 291840, 750592, 1890304, 4677632, 11403264, 27443200, 65306624, 153878528, 359399424, 832831488, 1916272640, 4380950528, 9957277696, 22510829568, 50642026496, 113413980160

Offset: 0

Author

Antti Karttunen, Aug 11 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A014480, A073345, A073773, A073775.

Programs

Maple

A073774 := n -> `if`((n < 3),0,(2^(n-2))*abs(A073775(n-3)));

Formula

a(n) = A073345(n+3, n).

a(n < 3) = 0, a(3) = 4, a(n) = 1/12 * 2^(n-1) * (2*n^3 + 9*n^2 - 23*n - 78) or a(n) = 2^(n-2) * |A073775(n-3)| from n >= 3 onward.