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A218265 Number of standard Young tableaux of n cells and height >= 5.

%I A218265 #18 Feb 08 2017 20:25:21
%S A218265 1,6,36,176,856,3952,18272,83524,384463,1777010,8304636,39254076,
%T A218265 188160268,915651672,4527595824,22771294440,116496899100,606656445480,
%U A218265 3214574890480,17337658462800,95128543350576,530998366724576,3013524116661952,17385349086129304
%N A218265 Number of standard Young tableaux of n cells and height >= 5.
%C A218265 Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 5. a(5)=1: 12345; a(6)=6: 123456, 123465, 123546, 124356, 132456, 213456.
%H A218265 Alois P. Heinz, <a href="/A218265/b218265.txt">Table of n, a(n) for n = 5..800</a>
%H A218265 Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>
%H A218265 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A218265 a(n) = A000085(n) - A005817(n) = A182172(n,n) - A182172(n,4).
%p A218265 a:= proc(n) option remember; `if`(n<13,
%p A218265       [0$5, 1, 6, 36, 176, 856, 3952, 18272, 83524][n+1],
%p A218265       ((n^4-2*n^3-179*n^2+256*n+804) *a(n-1)
%p A218265       +(n-1)*(n^4+6*n^3-295*n^2+1108*n+100) *a(n-2)
%p A218265       -4*(n-1)*(n-2)*(6*n^2-83*n+67) *a(n-3)
%p A218265       -16*(n-11)*(n-1)*(n-3)*(n-2)^2 *a(n-4))/
%p A218265       ((n-12)*(n-5)*(n+4)*(n+3)))
%p A218265     end:
%p A218265 seq(a(n), n=5..30);
%Y A218265 Column k=5 of A182222.
%K A218265 nonn
%O A218265 5,2
%A A218265 _Alois P. Heinz_, Oct 24 2012