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

Author

Michael Somos, Feb 08 2004

Keywords

• nonn
• tabl

Examples

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

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

Crossrefs

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

Main diagonal gives A120485.

Programs

PARI

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

Formula

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