A087727 Triangle read by rows: T(n,k) = (2 * (binomial(n,k)) * (n + 2 * k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!).

1, 1, 5, 1, 14, 42, 1, 28, 210, 462, 1, 48, 660, 3432, 6006, 1, 75, 1650, 15015, 60060, 87516, 1, 110, 3575, 50050, 340340, 1108536, 1385670, 1, 154, 7007, 140140, 1429428, 7759752, 21339318, 23371634, 1, 208, 12740, 346528, 4938024, 39504192, 178474296, 424938800, 414315330

Offset: 0

Author

Bill Gosper, Sep 30 2003

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1;
  1,  5;
  1, 14,  42;
  1, 28, 210, 462;
  ...
		

Crossrefs

Row sums give A087659. Right diagonal gives A005789.

Programs

PARI

t(n, k) = (2 * (binomial(n,k)) * (n + 2*k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!) \\ Michel Marcus, Jun 26 2013

Extensions

More terms from Ray Chandler, Sep 30 2003