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A141696 Triangle read by rows, T(n, k) = ( ( 6 * Sum_{j=0..k+1} (-1)^j * binomial(n+1, j) * (k-j+1)^n ) - 4 * binomial(n-1, k) ) / 2.

%I A141696 #16 Jun 10 2018 20:42:42
%S A141696 1,1,1,1,8,1,1,27,27,1,1,70,186,70,1,1,161,886,886,161,1,1,348,3543,
%T A141696 7208,3543,348,1,1,727,12837,46787,46787,12837,727,1,1,1490,43768,
%U A141696 264590,468430,264590,43768,1490,1,1,3021,143448,1365408,3930810
%N A141696 Triangle read by rows, T(n, k) = ( ( 6 * Sum_{j=0..k+1} (-1)^j * binomial(n+1, j) * (k-j+1)^n ) - 4 * binomial(n-1, k) ) / 2.
%H A141696 G. C. Greubel, <a href="/A141696/b141696.txt">Rows n=1..100 of triangle, flattened</a>
%e A141696 {1},
%e A141696 {1, 1},
%e A141696 {1, 8, 1},
%e A141696 {1, 27, 27, 1},
%e A141696 {1, 70, 186, 70, 1},
%e A141696 {1, 161, 886, 886, 161, 1},
%e A141696 {1, 348, 3543, 7208, 3543, 348, 1},
%e A141696 {1, 727, 12837, 46787, 46787, 12837, 727, 1},
%e A141696 {1, 1490, 43768, 264590, 468430, 264590, 43768, 1490, 1},
%e A141696 {1, 3021, 143448, 1365408, 3930810, 3930810, 1365408, 143448, 3021, 1}
%t A141696 i = 4; l = 6; Table[Table[(l*Sum[(-1)^j Binomial[n + 1, j](k + 1 -j)^n, {j, 0, k + 1}] - i*Binomial[n - 1, k])/2, {k, 0, n - 1}], {n, 1, 10}]; Flatten[%]
%o A141696 (PARI) {t(n,k) = (6*sum(j=0, k+1, (-1)^j*binomial(n+1,j)*(k-j+1)^n) - 4* binomial(n-1,k))/2};
%o A141696 for(n=1,10, for(k=0,n-1, print1(t(n,k), ", "))) \\ _G. C. Greubel_, Jun 03 2018
%Y A141696 Cf. Eulerian numbers (A008292) and Pascal's triangle (A007318).
%Y A141696 Cf. A141697.
%K A141696 nonn,easy,less,tabl
%O A141696 1,5
%A A141696 _Roger L. Bagula_, Sep 11 2008
%E A141696 Edited by the Associate Editors of the OEIS, Jun 10 2018