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A218264
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Number of standard Young tableaux of n cells and height >= 4.
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2
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1, 5, 25, 105, 441, 1785, 7308, 29898, 124641, 526669, 2276846, 10038964, 45353269, 209442533, 990777442, 4791502156, 23707812077, 119810145337, 618483875689, 3256714122209, 17488997849803, 95671400358075, 532959538382100, 3020603738202750, 17411069344112895
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OFFSET
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4,2
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COMMENTS
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Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 4. a(4)=1: 1234; a(5)=5: 12345, 12354, 12435, 13245, 21345.
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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<5, [0$4, 1][n+1], ((-5-7*n+3*n^2)*a(n-1)
+(n-1)*(n^2-n-11)*a(n-2) -2*n*(n-1)*(n-2)*a(n-3)
-3*(n-1)*(n-2)*(n-3)*a(n-4))/((n+2)*(n-4)))
end:
seq(a(n), n=4..30);
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MATHEMATICA
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a[n_] := a[n] = If[n<5, {0, 0, 0, 0, 1}[[n+1]], ((-5-7n+3n^2)a[n-1] + (n-1)(n^2-n-11)a[n-2] - 2n(n-1)(n-2)a[n-3] - 3(n-1)(n-2)(n-3)a[n-4])/ ((n+2)(n-4))];
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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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