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A218269
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Number of standard Young tableaux of n cells and height >= 9.
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2
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1, 10, 100, 760, 5656, 38416, 257376, 1660416, 10640692, 67100072, 422374352, 2643349180, 16566306380, 103786892840, 652502735152, 4113403313016, 26057914447911, 165824119892086, 1061381766546172, 6832087071296824, 44260892997918920, 288574772339715376
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OFFSET
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9,2
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COMMENTS
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Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 9.
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LINKS
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FORMULA
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MAPLE
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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);
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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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