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A067228
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Number of rectangular standard Young tableaux with n cells.
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3
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1, 2, 2, 4, 2, 12, 2, 30, 44, 86, 2, 1190, 2, 860, 12014, 26886, 2, 184758, 2, 3359202, 2771342, 117574, 2, 327618902, 701149022, 1485802, 828630662, 27350160662, 2, 808310933492, 2, 2979826568702, 291724349282, 259289582, 557214344578322, 2031957220875002, 2
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OFFSET
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1,2
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COMMENTS
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Number of ways to arrange the numbers 1, 2, .., n=i*j into an i*j rectangle so that each row and each column is increasing.
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LINKS
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FORMULA
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a(n) = n! * Sum_{i|n} Product_{k=0..n/i-1} k!/(i+k)!. - Alois P. Heinz, Jul 25 2012
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MAPLE
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with(numtheory):
a:= n-> n! * add(mul(k!/(i+k)!, k=0..(n/i)-1), i=divisors(n)):
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MATHEMATICA
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a[n_] := n! * Sum[Product[k!/(i+k)!, {k, 0, n/i-1}], {i, Divisors[n]}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 02 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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