%I A073773
%S A073773 0,0,0,6,40,152,480,1376,3712,9600,24064,58880,141312,333824,778240,
%T A073773 1794048,4096000,9273344,20840448,46530560,103284736,228065280,
%U A073773 501219328,1096810496,2390753280,5192548352,11240734720,24259854336
%N A073773 Number of plane binary trees of size n+2 and height n.
%H A073773 H. Bottomley & A. Karttunen <a href="a073345.txt">Derivations of the 
               formulae for the diagonals of A073345 & A073346.</a>
%F A073773 a(n < 3) = 0, a(n) = ((n^2 - 6)*2^(n-2))
%e A073773 a(3) = 6 because there exists only these six binary trees of size 5 and 
               height 3:
%e A073773 _\/\/_______\/\/_\/_\/_____\/_\/_\/___\/___V_V___
%e A073773 __\/_\/___\/_\/___\/_\/___\/_\/___\/_\/___\/_\/__
%e A073773 ___\./_____\./_____\./_____\./_____\./_____\./___
%p A073773 A073773 := n -> `if`((n < 3),0,((n^2 - 6)*2^(n-2)));
%Y A073773 A073773(n) = A073345(n+2, n). Cf. A014480, A073774, A028878.
%Y A073773 Sequence in context: A002595 A089207 A027777 this_sequence A001919 A005553 
               A055344
%Y A073773 Adjacent sequences: A073770 A073771 A073772 this_sequence A073774 A073775 
               A073776
%K A073773 nonn
%O A073773 0,4
%A A073773 Antti Karttunen Aug 11 2002