A095677 Triangle T(n,k), 0<=k<=n, read by rows, defined by Sum_{k = 0..n} T(n,k)*x^k = Sum_{k = 0..n} binomial(n,k)*(x+k)^n.

1, 1, 2, 6, 8, 4, 54, 72, 36, 8, 680, 896, 480, 128, 16, 11000, 14400, 8000, 2400, 400, 32, 217392, 283392, 161280, 51840, 10080, 1152, 64, 5076400, 6598144, 3819648, 1285760, 274400, 37632, 3136, 128, 136761984, 177373184, 103993344

Offset: 0

Author

Philippe Deléham Jul 04 2004

Keywords

• nonn
• tabl

Examples

			1; 1, 2; 6, 8, 4; 54, 72, 36, 8; 680, 896, 480, 128, 16; ...
		

Formula

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

T(n, n) = 2^n, see A000079.

T(n+1, n) = (n+1)^2*2^n, see A014477.

T(n, 0) = n*Sum_{k = 0..n-1} T(n-1, k).