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A218268 Number of standard Young tableaux of n cells and height >= 8.

%I A218268 #16 Feb 10 2017 08:16:45
%S A218268 1,9,81,561,3817,23881,147862,886028,5288933,31178901,183908244,
%T A218268 1081452450,6381113064,37719710024,224141652938,1337958249446,
%U A218268 8038507929319,48593807722975,295913856459150,1814986751559300,11220842616565050,69921225307663290
%N A218268 Number of standard Young tableaux of n cells and height >= 8.
%C A218268 Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 8. a(8)=1: 12345678; a(9)=9: 123456789, 123456798, 123456879, 123457689, 123465789, 123546789, 124356789, 132456789, 213456789.
%H A218268 Alois P. Heinz, <a href="/A218268/b218268.txt">Table of n, a(n) for n = 8..300</a>
%H A218268 Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>
%H A218268 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A218268 a(n) = A000085(n) - A007578(n) = A182172(n,n) - A182172(n,7).
%p A218268 b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
%p A218268 g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
%p A218268       ((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n
%p A218268       +305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1)
%p A218268       *(n-2)*(n-3)*g(n-4)) / ((n+6)*(n+10)*(n+12)))
%p A218268     end:
%p A218268 a:= n-> b(n) -g(n):
%p A218268 seq(a(n), n=8..30);
%Y A218268 Column k=8 of A182222.
%K A218268 nonn
%O A218268 8,2
%A A218268 _Alois P. Heinz_, Oct 24 2012