A225054 - OEIS

A225054

Triangle read by rows: Eulerian numbers T(n, k) = A173018(n + 1, 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, 6, 9, 11, 3, 1

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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..77.

Eric Weisstein's World of Mathematics, Eulerian Number

FORMULA

T(n,m) = Eulerian(n+1,m) mod (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. A173018, 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

EXTENSIONS

Definition amended by Georg Fischer, Nov 02 2025

STATUS

approved