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A218265
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Number of standard Young tableaux of n cells and height >= 5.
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2
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1, 6, 36, 176, 856, 3952, 18272, 83524, 384463, 1777010, 8304636, 39254076, 188160268, 915651672, 4527595824, 22771294440, 116496899100, 606656445480, 3214574890480, 17337658462800, 95128543350576, 530998366724576, 3013524116661952, 17385349086129304
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OFFSET
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5,2
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COMMENTS
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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.
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LINKS
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FORMULA
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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