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.
1, 1, 1, 1, 8, 1, 1, 27, 27, 1, 1, 70, 186, 70, 1, 1, 161, 886, 886, 161, 1, 1, 348, 3543, 7208, 3543, 348, 1, 1, 727, 12837, 46787, 46787, 12837, 727, 1, 1, 1490, 43768, 264590, 468430, 264590, 43768, 1490, 1, 1, 3021, 143448, 1365408, 3930810
Offset: 1
Examples
{1},
{1, 1},
{1, 8, 1},
{1, 27, 27, 1},
{1, 70, 186, 70, 1},
{1, 161, 886, 886, 161, 1},
{1, 348, 3543, 7208, 3543, 348, 1},
{1, 727, 12837, 46787, 46787, 12837, 727, 1},
{1, 1490, 43768, 264590, 468430, 264590, 43768, 1490, 1},
{1, 3021, 143448, 1365408, 3930810, 3930810, 1365408, 143448, 3021, 1}
Links
- G. C. Greubel, Rows n=1..100 of triangle, flattened
Programs
-
Mathematica
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[%] -
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}; for(n=1,10, for(k=0,n-1, print1(t(n,k), ", "))) \\ G. C. Greubel, Jun 03 2018
Extensions
Edited by the Associate Editors of the OEIS, Jun 10 2018