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A218265 Number of standard Young tableaux of n cells and height >= 5. 2
1, 6, 36, 176, 856, 3952, 18272, 83524, 384463, 1777010, 8304636, 39254076, 188160268, 915651672, 4527595824, 22771294440, 116496899100, 606656445480, 3214574890480, 17337658462800, 95128543350576, 530998366724576, 3013524116661952, 17385349086129304 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 5. a(5)=1: 12345; a(6)=6: 123456, 123465, 123546, 124356, 132456, 213456.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..800

Wikipedia, Involution (mathematics)

Wikipedia, Young tableau

FORMULA

a(n) = A000085(n) - A005817(n) = A182172(n,n) - A182172(n,4).

MAPLE

a:= proc(n) option remember; `if`(n<13,

      [0$5, 1, 6, 36, 176, 856, 3952, 18272, 83524][n+1],

      ((n^4-2*n^3-179*n^2+256*n+804) *a(n-1)

      +(n-1)*(n^4+6*n^3-295*n^2+1108*n+100) *a(n-2)

      -4*(n-1)*(n-2)*(6*n^2-83*n+67) *a(n-3)

      -16*(n-11)*(n-1)*(n-3)*(n-2)^2 *a(n-4))/

      ((n-12)*(n-5)*(n+4)*(n+3)))

    end:

seq(a(n), n=5..30);

CROSSREFS

Column k=5 of A182222.

Sequence in context: A200573 A224130 A283197 * A258629 A294465 A074444

Adjacent sequences:  A218262 A218263 A218264 * A218266 A218267 A218268

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 24 2012

STATUS

approved

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Last modified October 26 06:52 EDT 2021. Contains 348257 sequences. (Running on oeis4.)