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

1,1

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,....

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

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;

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[%]

Crossrefs

Cf. A046899, A178300, A001791

Sequence in context: A298299 A352597 A110765 * A264666 A283362 A337524

Adjacent sequences: A176988 A176989 A176990 * A176992 A176993 A176994

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 08 2010

Status

approved