A225054 Triangle read by rows: Eulerian numbers T(n,k) = A008292(n,k) reduced mod n+1.

0, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 3, 3, 5, 7, 1, 1, 7, 1, 7, 4, 7, 1, 7, 1, 1, 3, 0, 2, 4, 4, 2, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 9, 6, 6, 6

Offset: 0

Author

Roger L. Bagula, Apr 26 2013

Keywords

• nonn
• tabl

Comments

The row sums are:

{0, 2, 3, 8, 5, 12, 7, 32, 36, 20, 11, 72, 13,...}

Examples

			Triangle begins:
  {0},
  {1,1},
  {1,1,1},
  {1,3,3,1},
  {1,1,1,1,1},
  {1,3,2,2,3,1},
  {1,1,1,1,1,1,1},
  {1,7,5,3,3,5,7,1},
  {1,7,1,7,4,7,1,7,1},
  {1,3,0,2,4,4,2,0,3,1},
  {1,1,1,1,1,1,1,1,1,1,1},
  {1,3,11,9,6,6,6,6,9,11,3,1},
  {1,1,1,1,1,1,1,1,1,1,1,1,1},
  ...
		

Links

• Eric Weisstein's World of Mathematics, Eulerian Number

Crossrefs

Cf. A008292, A225043.

Programs

Mathematica

Flatten[Table[Table[Mod[Eulerian[n+1,m],n+1],{m,0,n}],{n,0,12}]]

Formula

T(n,m) = Eulerian(n+1,m) mod (n+1).