A225419 Triangle read by rows: T(n,k) (0 <= k <= n) = binomial(2*n+2,k).

1, 1, 4, 1, 6, 15, 1, 8, 28, 56, 1, 10, 45, 120, 210, 1, 12, 66, 220, 495, 792, 1, 14, 91, 364, 1001, 2002, 3003, 1, 16, 120, 560, 1820, 4368, 8008, 11440, 1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 1, 20, 190

Offset: 0

Author

Roger L. Bagula, May 07 2013

Keywords

• nonn
• tabl
• easy

Comments

Row sums are A000346.

Examples

			Triangle begins:
1,
1, 4,
1, 6, 15,
1, 8, 28, 56,
1, 10, 45, 120, 210,
1, 12, 66, 220, 495, 792,
1, 14, 91, 364, 1001, 2002, 3003,
...
		

Links

• Roger L. Bagula, a225419nb.txt

Crossrefs

Cf. A127673, A062344, A034870, A000346.

Programs

Mathematica

Flatten[Table[Table[DifferenceRoot[Function[{y, n}, {(-(2*m + 1) + n) y[n] + n y[1 + n] == 0, y[1] == 1}]][k], {k, 1, m}], {m, 1, 10}]]
Flatten[Table[Binomial[2n+2,k],{n,0,10},{k,0,n}]] (* Harvey P. Dale, Apr 13 2014 *)

Extensions

Edited by N. J. A. Sloane, May 11 2013