A086872 Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.

1, 1, 1, 3, 8, 5, 15, 75, 121, 61, 105, 840, 2478, 3128, 1385, 945, 11025, 51030, 115350, 124921, 50521, 10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765

Offset: 0

Author

Philippe Deléham, Aug 20 2003, Aug 17 2007

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
1;
1, 1;
3, 8, 5;
15, 75, 121, 61;
105, 840, 2478, 3128, 1385;
945, 11025, 51030, 115350, 124921, 50521;
10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765 ; ...
		

Links

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

Crossrefs

Cf. A000182 (row sums), A000364 (first diagonal), A001147 (first column), A084938, A261065 (2nd column).

Formula

Sum( k>=0, T(n, k)*(-1)^k ) = 0; if n>0.

Sum( k>=0, T(n, k)*(-1/2)^k ) = (1/2)^n.

Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = (-1)^n*A121822(n), (-1)^n*A092812(n), (-1)^n*A054879(n), A009117(n), A033999(n), A000007(n), A000364(n), A000182(n+1) for x = -6, -5, -4, -3, -2, -1, 0, 1 respectively .