A109450 - OEIS

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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

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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