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A218268 Number of standard Young tableaux of n cells and height >= 8. 2
1, 9, 81, 561, 3817, 23881, 147862, 886028, 5288933, 31178901, 183908244, 1081452450, 6381113064, 37719710024, 224141652938, 1337958249446, 8038507929319, 48593807722975, 295913856459150, 1814986751559300, 11220842616565050, 69921225307663290 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

COMMENTS

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..300

Wikipedia, Involution (mathematics)

Wikipedia, Young tableau

FORMULA

a(n) = A000085(n) - A007578(n) = A182172(n,n) - A182172(n,7).

MAPLE

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

g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],

      ((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n

      +305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1)

      *(n-2)*(n-3)*g(n-4)) / ((n+6)*(n+10)*(n+12)))

    end:

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

seq(a(n), n=8..30);

CROSSREFS

Column k=8 of A182222.

Sequence in context: A207009 A196986 A293889 * A223882 A267961 A213297

Adjacent sequences:  A218265 A218266 A218267 * A218269 A218270 A218271

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 24 2012

STATUS

approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)