cp's OEIS Frontend

A368567 Number of Young tableaux of shape [n, floor(n/2)].

%I A368567 #27 Jun 01 2025 16:35:00
%S A368567 1,1,2,3,9,14,48,75,275,429,1638,2548,9996,15504,62016,95931,389367,
%T A368567 600875,2466750,3798795,15737865,24192090,100975680,154969620,
%U A368567 650872404,997490844,4211628008,6446369400,27341497800,41802112192,177996090624,271861216539,1161588834303,1772528290407,7596549816030,11582393855305
%N A368567 Number of Young tableaux of shape [n, floor(n/2)].
%C A368567 Seemingly also the number of Catalan words of length n with at least ceiling(n/2) zeros. - _Sela Fried_, Jun 01 2025
%H A368567 Alois P. Heinz, <a href="/A368567/b368567.txt">Table of n, a(n) for n = 0..2417</a>
%H A368567 Joerg Arndt, <a href="/A368567/a368567.txt">The a(6)=48 Young tableaux of shape [6,3] and a(7)=75 Young tableaux of shape [7,3]</a>.
%F A368567 a(2*n) = A174687(n/2), a(2*n+1) = A026004(n).
%p A368567 a:= proc(n) option remember; `if`(n<3, [1$2, 2][n+1],
%p A368567       (4*n*(3027*n^2-10201*n+4134)*a(n-1)+6*(729*n^3-6201*n^2+9177*n-4921)*
%p A368567       a(n-2)-3*(3*n-7)*(3027*n+1907)*(3*n-8)*a(n-3))/(8*(n+1)*n*(81*n-689)))
%p A368567     end:
%p A368567 seq(a(n), n=0..35);  # _Alois P. Heinz_, Jun 01 2025
%Y A368567 Cf. A174687 (shape [2*n, n]), A026004 (shape [2*n+1, n]).
%K A368567 nonn
%O A368567 0,3
%A A368567 _Joerg Arndt_, Dec 30 2023