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

1,5

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Example

{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}

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[%]

Prog

(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

Crossrefs

Cf. Eulerian numbers (A008292) and Pascal's triangle (A007318).

Cf. A141697.

Sequence in context: A176283 A323324 A181543 * A178122 A142470 A168523

Adjacent sequences: A141693 A141694 A141695 * A141697 A141698 A141699

Keyword

nonn,easy,less,tabl

Author

Roger L. Bagula, Sep 11 2008

Extensions

Edited by the Associate Editors of the OEIS, Jun 10 2018

Status

approved