This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A073773 #11 Mar 02 2024 10:37:25 %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 Henry Bottomley & Antti Karttunen <a href="/A073345/a073345.txt">Derivations of the formulas for the diagonals of A073345 & A073346</a>. %F A073773 a(n) = A073345(n+2, n). %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 Cf. A014480, A073345, A073774, A028878. %K A073773 nonn %O A073773 0,4 %A A073773 _Antti Karttunen_, Aug 11 2002