A176991 Triangle t(n,m) = binomial(n+m,m) - binomial(n-m,m), 1<=m<=n, read by rows.

2, 2, 6, 2, 10, 20, 2, 14, 35, 70, 2, 18, 56, 126, 252, 2, 22, 83, 210, 462, 924, 2, 26, 116, 330, 792, 1716, 3432, 2, 30, 155, 494, 1287, 3003, 6435, 12870, 2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620, 2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756

Offset: 1

Author

Roger L. Bagula, Dec 08 2010

Keywords

• nonn
• tabl

Comments

Row sums are binomial(2n+1,n+1)-1-A000071(n+1) = A001700(n)-A000045(n+1) = 2, 8, 32, 121, 454, 1703, 6414, 24276, 92323, 352627,....

Examples

			2;
2, 6;
2, 10, 20;
2, 14, 35, 70;
2, 18, 56, 126, 252;
2, 22, 83, 210, 462, 924;
2, 26, 116, 330, 792, 1716, 3432;
2, 30, 155, 494, 1287, 3003, 6435, 12870;
2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620;
2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756;
		

Crossrefs

Cf. A046899, A178300, A001791

Programs

Mathematica

t[n_, m_] = Binomial[n + (m - 1), (m - 1)] - Binomial[n - (m - 1), (m - 1)];
Table[Table[t[n, m], {m, 2, n + 1}], {n, 1, 10}];
Flatten[%]

Formula

t(n,m) = A046899(n,m) - A011973(n,m), 0<=m<=n/2.