A091884 Triangle of numbers defined by Knuth.

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, 12366942, 12360381, 12360637, 12360636, 12360636

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.

Links

Seiichi Manyama, Rows n = 0..139, flattened

Formula

T(n,k) = Sum_{j=0..k} (-1)^j * (n-j)^n.

Example

Triangle begins:
     1;
     1,    1;
     4,    3,    3;
    27,   19,   20,   20;
   256,  175,  191,  190,  190;
  3125, 2101, 2344, 2312, 2313, 2313;
  ...

Prog

(PARI) T(n, k)=if(k<0 || k>n, 0, sum(j=0, k, (-1)^j*(n-j)^n))

Crossrefs

Column k=0..1 give A000312, A045531.

Main diagonal gives A120485.

Sequence in context: A370574 A309046 A007568 * A255257 A306769 A336031

Adjacent sequences: A091881 A091882 A091883 * A091885 A091886 A091887

Keyword

nonn,tabl

Author

Michael Somos, Feb 08 2004

Status

approved