cp's OEIS Frontend

A218269 Number of standard Young tableaux of n cells and height >= 9.

%I A218269 #14 Feb 10 2017 08:17:17
%S A218269 1,10,100,760,5656,38416,257376,1660416,10640692,67100072,422374352,
%T A218269 2643349180,16566306380,103786892840,652502735152,4113403313016,
%U A218269 26057914447911,165824119892086,1061381766546172,6832087071296824,44260892997918920,288574772339715376
%N A218269 Number of standard Young tableaux of n cells and height >= 9.
%C A218269 Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 9.
%H A218269 Alois P. Heinz, <a href="/A218269/b218269.txt">Table of n, a(n) for n = 9..300</a>
%H A218269 Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>
%H A218269 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A218269 a(n) = A000085(n) - A007580(n) = A182172(n,n) - A182172(n,8).
%p A218269 b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
%p A218269 g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
%p A218269       ((40*n^3+1084*n^2+8684*n+18480)*g(n-1) +16*(n-1)
%p A218269       *(5*n^3+107*n^2+610*n+600)*g(n-2) -1024*(n-1)*(n-2)
%p A218269       *(n+6)*g(n-3) -1024*(n-1)*(n-2)*(n-3)*(n+4)*g(n-4))/
%p A218269        ((n+7)*(n+12)*(n+15)*(n+16)))
%p A218269     end:
%p A218269 a:= n-> b(n) -g(n):
%p A218269 seq(a(n), n=9..30);
%Y A218269 Column k=9 of A182222.
%K A218269 nonn
%O A218269 9,2
%A A218269 _Alois P. Heinz_, Oct 24 2012