A176991 - OEIS

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

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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, 6;

2, 10, 20;