Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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