A347823 Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.

1, 2, 3, 3, 8, 5, 4, 15, 18, 7, 5, 24, 42, 32, 9, 6, 35, 80, 90, 50, 11, 7, 48, 135, 200, 165, 72, 13, 8, 63, 210, 385, 420, 273, 98, 15, 9, 80, 308, 672, 910, 784, 420, 128, 17, 10, 99, 432, 1092, 1764, 1890, 1344, 612, 162, 19, 11, 120, 585, 1680, 3150, 4032, 3570, 2160, 855, 200, 21

Offset: 0

Author

Jules Beauchamp, Jan 23 2022

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  2,  3;
  3,  8,   5;
  4, 15,  18,   7;
  5, 24,  42,  32,   9;
  6, 35,  80,  90,  50,  11;
  7, 48, 135, 200, 165,  72, 13;
  8, 63, 210, 385, 420, 273, 98, 15;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Crossrefs

Row sums give A053220.

Columns give A000027, A005563, A212343.

Diagonals give A005408, A001105, A059270, A112742.

Cf. A007318, A094727.

Programs

PARI

T(n,k) = (n+k+1)*binomial(n,k) \\ Andrew Howroyd, Jan 23 2022

Formula

T(n,k) = A094727(n+1,k)*A007318(n,k).

Row g.f.: (1 + x)^(n-1)*(1 + n + x + 2*n*x). - Stefano Spezia, Jan 23 2022