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A271707
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Triangle read by rows, T(n,k) = Sum_{p in P(n,k)} Aut(p) where P(n,k) are the partitions of n with length k and Aut(p) = 1^j[1]*j[1]!*...*n^j[n]*j[n]! where j[m] is the number of parts in the partition p equal to m; for n>=0 and 0<=k<=n.
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1
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1, 0, 1, 0, 2, 2, 0, 3, 2, 6, 0, 4, 11, 4, 24, 0, 5, 10, 14, 12, 120, 0, 6, 31, 62, 34, 48, 720, 0, 7, 28, 60, 84, 120, 240, 5040, 0, 8, 66, 102, 490, 228, 552, 1440, 40320, 0, 9, 60, 299, 292, 708, 912, 3120, 10080, 362880, 0, 10, 120, 282, 722, 4396, 2136, 4752, 20880, 80640, 3628800
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OFFSET
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0,5
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COMMENTS
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S(n,k) = Sum_{p in P(n,k)} n!/Aut(p) are the Stirling cycle numbers A132393.
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LINKS
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EXAMPLE
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Triangle starts:
[1]
[0, 1]
[0, 2, 2]
[0, 3, 2, 6]
[0, 4, 11, 4, 24]
[0, 5, 10, 14, 12, 120]
[0, 6, 31, 62, 34, 48, 720]
[0, 7, 28, 60, 84, 120, 240, 5040]
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PROG
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(Sage)
P = Partitions(n, length=k)
return sum(p.aut() for p in P)
for n in (0..10): print([A271707(n, k) for k in (0..n)])
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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