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A218266 Number of standard Young tableaux of n cells and height >= 6.

%I A218266 #16 Feb 10 2017 08:15:31
%S A218266 1,7,49,273,1506,7788,40161,202917,1028170,5190328,26375635,134565795,
%T A218266 692890250,3596739368,18877483060,100131220940,537718999715,
%U A218266 2922918175965,16100254700137,89857257410905,508473405642250,2916903963927300,16969580464205400
%N A218266 Number of standard Young tableaux of n cells and height >= 6.
%C A218266 Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 6. a(6)=1: 123456; a(7)=7: 1234567, 1234576, 1234657, 1235467, 1243567, 1324567, 2134567.
%H A218266 Alois P. Heinz, <a href="/A218266/b218266.txt">Table of n, a(n) for n = 6..300</a>
%H A218266 Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>
%H A218266 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A218266 a(n) = A000085(n) - A049401(n) = A182172(n,n) - A182172(n,5).
%p A218266 b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
%p A218266 g:= proc(n) option remember; `if`(n<3, [1, 1, 2][n+1],
%p A218266       ((3*n^2+17*n+15)*g(n-1) +(n-1)*(13*n+9)*g(n-2)
%p A218266        -15*(n-1)*(n-2)*g(n-3)) / ((n+4)*(n+6)))
%p A218266     end:
%p A218266 a:= n-> b(n) -g(n):
%p A218266 seq(a(n), n=6..30);
%Y A218266 Column k=6 of A182222.
%K A218266 nonn
%O A218266 6,2
%A A218266 _Alois P. Heinz_, Oct 24 2012