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A089231
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Triangular array A066667 or A008297 unsigned and transposed.
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0
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1, 1, 2, 1, 6, 6, 1, 12, 36, 24, 1, 20, 120, 240, 120, 1, 30, 300, 1200, 1800, 720, 1, 42, 630, 4200, 12600, 15120, 5040, 1, 56, 1176, 11760, 58800, 141120, 141120, 40320, 1, 72, 2016, 28224, 211680, 846720, 1693440, 1451520, 362880
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums: A000262
T(n, k) is also the number of nilpotent partial one-one bijections (of an n-element set) of of height k (height(alpha) = |Im(alpha)|). [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]
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REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 203.
Ganyushkin, Olexandr; Mazorchuk, Volodymyr Combinatorics of nilpotents in symmetric inverse semigroups. Ann. Comb. 8 (2004), no. 2, 161--175. [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]
Laradji, A. and Umar, A. On the number of nilpotents in the partial symmetric semigroup. Comm. Algebra 32 (2004), 3017-3023. [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]
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LINKS
| F. Hivert, J.-C. Novelli and J.-Y. Thibon, Commutative combinatorial Hopf algebras
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FORMULA
| T(n, k) = A001263(n, k)*k!; A001263 = triangle of Narayana.
T(n, k) = C(n, n-k+1)*(n-1)!/(n-k)! = Sum[i=n-k+1..n, |S1(n, i)S2(i, n-k+1)| ], with S1, S2 the Stirling numbers.
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CROSSREFS
| Cf. A008297 A066667 A000262.
Sequence in context: A046651 A063007 A202190 * A052296 A019538 A046521
Adjacent sequences: A089228 A089229 A089230 * A089232 A089233 A089234
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 10 2003
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