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

0,8

Comments

The row sums are:

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

Links

Table of n, a(n) for n=0..72.

Eric Weisstein's World of Mathematics, Eulerian Number

Formula

t(n,m)=Mod(Eulerian(n+1,m),n+1)

Example

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}},
...

Mathematica

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

Crossrefs

Cf. A008292, A225043.

Sequence in context: A283797 A059441 A186028 * A355604 A059790 A307156

Adjacent sequences: A225051 A225052 A225053 * A225055 A225056 A225057

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 26 2013

Status

approved