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A101818
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Triangle read by rows: (1/n)*T(n,h), where T(n,h) is the array in A101817.
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3
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1, 1, 1, 1, 6, 2, 1, 21, 36, 6, 1, 60, 300, 240, 24, 1, 155, 1800, 3900, 1800, 120, 1, 378, 9030, 42000, 50400, 15120, 720, 1, 889, 40572, 357210, 882000, 670320, 141120, 5040, 1, 2040, 169400, 2610720, 11677680, 17781120, 9313920, 1451520, 40320
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OFFSET
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1,5
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COMMENTS
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T(n,h) is the number of partial functions f:{1,2,...,n-1}->{1,2,...,n-1} such that |Image(f)| = h-1. Equivalently T(n,h) = |D_h(a)| where D_h(a) is Green's D-class containing a, with a in the semigroup of partial transformations on [n-1] and rank(a) = h-1. - Geoffrey Critzer, Jan 02 2022
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REFERENCES
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O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, 2009, page 61.
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LINKS
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FORMULA
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T(n, h) = (1/n)*C(n, h)*U(n, h), where U(n, h) is the array in A019538.
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EXAMPLE
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First rows:
1
1 1
1 6 2
1 21 36 6
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MATHEMATICA
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Table[Table[StirlingS2[n, k] (n-1)!/(n - k)!, {k, 1, n}], {n, 1,
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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