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Search: id:A132795
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| A132795 |
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Triangle of Gely numbers, read by rows. |
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+0
2
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| 1, 1, 0, 1, 0, 1, 1, 0, 5, 0, 1, 0, 16, 6, 1, 1, 0, 42, 56, 21, 0, 1, 0, 99, 316, 267, 36, 1, 1, 0, 219, 1408, 2367, 960, 85, 0, 1, 0, 466, 5482, 16578, 14212, 3418, 162, 1, 1, 0, 968, 19624, 99330, 153824, 77440, 11352, 341, 0, 1, 0, 1981, 66496, 534898, 1364848
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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First row is for n=0. First column is for k=0.
Sum of rows is n! = permutations of n symbols (A0xxxx)
These numbers are related to the Eulerian numbers A(n,k).
Third Column (k=2) is A002662(n+1).
Second Diagonal (k=n-1) is A132796.
Binomial transform of this triangle gives set partitions without singletons (in a form very close to array A105794).
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REFERENCES
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Charles 0. Gely, Un tableau de conversion des polynomes cyclotomiques cousin des nombres Euleriens, Preprint Univ. Paris 7, 1999.
Olivier Gerard, Quelques facons originales de compter les permutations, submitted to Knuth07.
Olivier Gerard and Karol Penson, Set partitions, Multiset permutations and bi-permutations, in preparation.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics= . Addison-Wesley, Reading, MA, 1990, p. 269.
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FORMULA
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T(n,k)= Sum((-1)^j (n+1 choose j) (1-(k-j)^(n+1))/(1-(k-j)), 0<=j<=k).
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CROSSREFS
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Cf. A132796, A000296.
Sequence in context: A068385 A071086 A060338 this_sequence A085198 A058064 A104112
Adjacent sequences: A132792 A132793 A132794 this_sequence A132796 A132797 A132798
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com), Aug 31, 2007
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