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

0,6

Comments

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

Transposed version in A107842.

Links

Table of n, a(n) for n=0..59.

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.

Example

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.

Sequence in context: A085650 A343751 A201910 * A086810 A085838 A094456

Adjacent sequences: A109447 A109448 A109449 * A109451 A109452 A109453

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Aug 26 2005

Status

approved