A073774 - OEIS

%I #13 Mar 02 2024 10:37:31

%S 0,0,0,4,68,376,1440,4736,14272,40576,110592,291840,750592,1890304,

%T 4677632,11403264,27443200,65306624,153878528,359399424,832831488,

%U 1916272640,4380950528,9957277696,22510829568,50642026496,113413980160

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

%H Henry Bottomley and Antti Karttunen, <a href="/A073345/a073345.txt">Derivations of the formulas for the diagonals of A073345 & A073346</a>.

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

%F 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.

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

%Y Cf. A014480, A073345, A073773, A073775.

%K nonn

%O 0,4

%A _Antti Karttunen_, Aug 11 2002