|
| |
|
|
A091884
|
|
Triangle of numbers defined by Knuth.
|
|
0
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
REFERENCES
| 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.
|
|
|
FORMULA
| T(n, k)=sum_{j=0}^k binomial(k, j)(-1)^j(n-j)^n.
|
|
|
EXAMPLE
| {1},{1,1},{4,3,3},{27,19,20,20},{256,175,191,190,190},...
|
|
|
PROG
| (PARI) T(n, k)=if(k<0|k>n, 0, sum(j=0, k, (-1)^j*(n-j)^n))
|
|
|
CROSSREFS
| Sequence in context: A138187 A055525 A007568 * A048156 A070431 A070511
Adjacent sequences: A091881 A091882 A091883 * A091885 A091886 A091887
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Michael Somos, Feb 08 2004
|
| |
|
|
