A215080 T(n,k) = Sum_{j=0..k} (k-j)^n * binomial(n,j).

1, 0, 1, 0, 1, 6, 0, 1, 11, 54, 0, 1, 20, 151, 680, 0, 1, 37, 413, 2569, 11000, 0, 1, 70, 1128, 9450, 52431, 217392, 0, 1, 135, 3104, 34416, 243255, 1251921, 5076400, 0, 1, 264, 8637, 125248, 1113027, 7025016, 34282879, 136761984, 0, 1, 521, 24327, 457807, 5064143, 38811015, 225930121, 1059812993, 4175432064, 0, 1, 1034, 69334, 1685266, 23031680, 212609518, 1465077802, 8026643702, 36519075583, 142469423360

Offset: 0

Author

Olivier Gérard, Aug 02 2012

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1;
  0, 1;
  0, 1,   6;
  0, 1,  11,   54;
  0, 1,  20,  151,    680;
  0, 1,  37,  413,   2569,   11000;
  0, 1,  70, 1128,   9450,   52431,  217392;
  0, 1, 135, 3104,  34416,  243255, 1251921,  5076400;
  0, 1, 264, 8637, 125248, 1113027, 7025016, 34282879, 136761984;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Row sums give 215077 (binomial convolution of descending powers).

Main diagonal gives A072034.

Programs

Mathematica

Flatten[Table[Table[Sum[(k - j)^n*Binomial[n, j], {j, 0, k}], {k, 0, n}], {n, 0, 10}], 1]

Formula

T(n,k) = sum( (k-j)^n * binomial(n,j), j=0..k).