A109450 Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 2, 0, 1, 5, 5, 0, 1, 8, 20, 14, 0, 1, 11, 44, 75, 42, 0, 1, 14, 77, 208, 275, 132, 0, 1, 17, 119, 440, 910, 1001, 429, 0, 1, 20, 170, 798, 2244, 3808, 3640, 1430, 0, 1, 23, 230, 1309, 4655, 10659, 15504, 13260, 4862, 0, 1, 26, 299, 2000

Offset: 0

Author

Philippe Deléham, Aug 26 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums : 1, 1, 3, 11, 43, 173, .... (see A026671).

Transposed version in A107842.

Examples

			Triangle begins:
1;
0, 1;
0, 1, 2;
0, 1, 5, 5;
0, 1, 8, 20, 14;
0, 1, 11, 44, 75, 42;
0, 1, 14, 77, 208, 275, 132
		

Crossrefs

Cf. A000108, A000344, A003518, A000589, A107842.

Formula

T(0, 0) = 1, T(n, 0) = 0 if n>0, T(n, k) = 0 if k>n, T(n, k) = (3n-3k+2)*binomial(3n-k-1, k-1)/(3n-2k+1).

T(n, n) = A000108(n), Catalan numbers.