A218267 - OEIS

%I #16 Feb 10 2017 08:16:20

%S 1,8,64,400,2465,14092,80016,442248,2442351,13375366,73477622,

%T 403703404,2230591660,12380801756,69225756076,389806286920,

%U 2213844625658,12681996193252,73339826141716,428242854338216,2526129602115517,15056977593085444,90712249806247400

%N Number of standard Young tableaux of n cells and height >= 7.

%C Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 7. a(7)=1: 1234567; a(8)=8: 12345678, 12345687, 12345768, 12346578, 12354678, 12435678, 13245678, 21345678.

%H Alois P. Heinz, <a href="/A218267/b218267.txt">Table of n, a(n) for n = 7..300</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%F a(n) = A000085(n) - A007579(n) = A182172(n,n) - A182172(n,6).

%p b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:

%p g:= proc(n) option remember;

%p       `if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*g(n-1)

%p        +4*(n-1)*(10*n^2+58*n+33)*g(n-2) -144*(n-1)*(n-2)*g(n-3)

%p        -144*(n-1)*(n-2)*(n-3)*g(n-4)) / ((n+5)*(n+8)*(n+9)))

%p     end:

%p a:= n-> b(n) -g(n):

%p seq(a(n), n=7..30);

%Y Column k=7 of A182222.

%K nonn

%O 7,2

%A _Alois P. Heinz_, Oct 24 2012