A193450 Triangle of a binomial convolution sum related to Jacobsthal numbers.

0, 1, 0, 2, 2, 2, 3, 6, 6, 0, 4, 12, 16, 8, 4, 5, 20, 35, 30, 15, 0, 6, 30, 66, 78, 54, 18, 6, 7, 42, 112, 168, 154, 84, 28, 0, 8, 56, 176, 320, 368, 272, 128, 32, 8, 9, 72, 261, 558, 774, 720, 450, 180, 45, 0, 10, 90, 370, 910, 1480, 1660, 1300, 700, 250, 50, 10

Offset: 0

Author

Olivier Gérard, Jul 26 2011

Keywords

• nonn
• easy
• tabl

Comments

Row sum is A193449(n) = A001045(n+1)*n.

Examples

			Triangle starts:
0;
1, 0;
2, 2, 2;
3, 6, 6, 0;
4, 12, 16, 8, 4;
5, 20, 35, 30, 15, 0;
...
		

Crossrefs

Cf. A193451.

Programs

PARI

T(n,k) = sum(j=0, k, (-1)^j*n*binomial(n-j,k-j)); \\ Michel Marcus, Jun 04 2014

Formula

T(n,k) = sum( (-1)^j*n*C(n-j,k-j), j=0..k).

T(n,k) = n*C(n, k)*2F1( (1, -k); -n )(-1).