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A218269 Number of standard Young tableaux of n cells and height >= 9. 2
1, 10, 100, 760, 5656, 38416, 257376, 1660416, 10640692, 67100072, 422374352, 2643349180, 16566306380, 103786892840, 652502735152, 4113403313016, 26057914447911, 165824119892086, 1061381766546172, 6832087071296824, 44260892997918920, 288574772339715376 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

COMMENTS

Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 9.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..300

Wikipedia, Involution (mathematics)

Wikipedia, Young tableau

FORMULA

a(n) = A000085(n) - A007580(n) = A182172(n,n) - A182172(n,8).

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],

      ((40*n^3+1084*n^2+8684*n+18480)*g(n-1) +16*(n-1)

      *(5*n^3+107*n^2+610*n+600)*g(n-2) -1024*(n-1)*(n-2)

      *(n+6)*g(n-3) -1024*(n-1)*(n-2)*(n-3)*(n+4)*g(n-4))/

       ((n+7)*(n+12)*(n+15)*(n+16)))

    end:

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

seq(a(n), n=9..30);

CROSSREFS

Column k=9 of A182222.

Sequence in context: A223920 A223865 A293890 * A224348 A213298 A224007

Adjacent sequences:  A218266 A218267 A218268 * A218270 A218271 A218272

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 24 2012

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)