A225043 -id:A225043 - cp's OEIS frontend

A320440 Row sums of A225043.

0, 2, 4, 8, 11, 20, 22, 32, 31, 52, 56, 80, 79, 100, 94, 128, 137, 176, 172, 208, 193, 244, 254, 320, 266, 340, 283, 400, 407, 332, 466, 512, 499, 580, 569, 680, 667, 724, 745, 848, 821, 872, 904, 976, 1021, 1060, 1082, 1280, 1093, 1312, 1330, 1360, 1379, 1472, 1479, 1584, 1543

Offset: 0

Nathan M Epstein, Jan 09 2019

nonn

Nathan M Epstein, Python program

Cf. A000040, A062173, A072205, A225043.

a[n_]:=Sum[Mod[Binomial[n, k],n+1], {k,0, n}]; Array[a, 100, 0] (* Stefano Spezia, Jan 09 2019 *)

a(n) = sum(k=0, n, binomial(n,k) % (n+1)); \\ Michel Marcus, Jan 09 2019

a(A000040(n)) = A072205(n) for n > 0.

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

Original entry on oeis.org

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

Roger L. Bagula, Apr 26 2013

The row sums are:

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

			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},
  ...

Eric Weisstein's World of Mathematics, Eulerian Number

Cf. A008292, A225043.

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

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

cp's OEIS Frontend

A320440 Row sums of A225043.

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