|
%I #11 Mar 02 2024 10:37:25
%S 0,0,0,6,40,152,480,1376,3712,9600,24064,58880,141312,333824,778240,
%T 1794048,4096000,9273344,20840448,46530560,103284736,228065280,
%U 501219328,1096810496,2390753280,5192548352,11240734720,24259854336
%N Number of plane binary trees of size n+2 and height n.
%H Henry Bottomley & Antti Karttunen <a href="/A073345/a073345.txt">Derivations of the formulas for the diagonals of A073345 & A073346</a>.
%F a(n) = A073345(n+2, n).
%F a(n < 3) = 0, a(n) = ((n^2 - 6)*2^(n-2)).
%e a(3) = 6 because there exists only these six binary trees of size 5 and height 3:
%e _\/\/_______\/\/_\/_\/_____\/_\/_\/___\/___V_V___
%e __\/_\/___\/_\/___\/_\/___\/_\/___\/_\/___\/_\/__
%e ___\./_____\./_____\./_____\./_____\./_____\./___
%p A073773 := n -> `if`((n < 3),0,((n^2 - 6)*2^(n-2)));
%Y Cf. A014480, A073345, A073774, A028878.
%K nonn
%O 0,4
%A _Antti Karttunen_, Aug 11 2002
|
