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Search: id:A091884
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| A091884 |
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Triangle of numbers defined by Knuth. |
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+0
1
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| 1, 1, 1, 4, 3, 3, 27, 19, 20, 20, 256, 175, 191, 190, 190, 3125, 2101, 2344, 2312, 2313, 2313, 46656, 31031, 35127, 34398, 34462, 34461, 34461, 823543, 543607, 621732, 605348, 607535, 607407, 607408, 607408, 16777216, 11012415, 12692031, 12301406
(list; table; graph; listen)
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OFFSET
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0,4
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REFERENCES
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.4 Answer to Exer. 46.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 101.
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FORMULA
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T(n, k)=sum_{j=0}^k binomial(k, j)(-1)^j(n-j)^n.
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EXAMPLE
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{1},{1,1},{4,3,3},{27,19,20,20},{256,175,191,190,190},...
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PROGRAM
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(PARI) T(n, k)=if(k<0|k>n, 0, sum(j=0, k, (-1)^j*(n-j)^n))
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CROSSREFS
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Sequence in context: A138187 A055525 A007568 this_sequence A048156 A070431 A070511
Adjacent sequences: A091881 A091882 A091883 this_sequence A091885 A091886 A091887
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KEYWORD
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nonn,tabl
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AUTHOR
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Michael Somos, Feb 08 2004
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