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

%I A225054 #11 Feb 16 2025 08:33:19
%S A225054 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,
%T A225054 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,
%U A225054 11,9,6,6,6
%N A225054 Triangle read by rows: Eulerian numbers T(n,k) = A008292(n,k) reduced mod n+1.
%C A225054 The row sums are:
%C A225054 {0, 2, 3, 8, 5, 12, 7, 32, 36, 20, 11, 72, 13,...}
%H A225054 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerianNumber.html">Eulerian Number</a>
%F A225054 T(n,m) = Eulerian(n+1,m) mod (n+1).
%e A225054 Triangle begins:
%e A225054   {0},
%e A225054   {1,1},
%e A225054   {1,1,1},
%e A225054   {1,3,3,1},
%e A225054   {1,1,1,1,1},
%e A225054   {1,3,2,2,3,1},
%e A225054   {1,1,1,1,1,1,1},
%e A225054   {1,7,5,3,3,5,7,1},
%e A225054   {1,7,1,7,4,7,1,7,1},
%e A225054   {1,3,0,2,4,4,2,0,3,1},
%e A225054   {1,1,1,1,1,1,1,1,1,1,1},
%e A225054   {1,3,11,9,6,6,6,6,9,11,3,1},
%e A225054   {1,1,1,1,1,1,1,1,1,1,1,1,1},
%e A225054   ...
%t A225054 Flatten[Table[Table[Mod[Eulerian[n+1,m],n+1],{m,0,n}],{n,0,12}]]
%Y A225054 Cf. A008292, A225043.
%K A225054 nonn,tabl
%O A225054 0,8
%A A225054 _Roger L. Bagula_, Apr 26 2013