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A156716
Let k=2; then T(n,m) = (((2*k+1)/(m+k+1))*binomial(n-1-k, m-k)*binomial(n+k, m+k) + ((2*k+1)/(n-m+k))*binomial(n-1-k, n-m-1-k)*binomial(n+k, n-m-1+k)), irregular triangle.
1
5, 0, 5, 5, 15, 15, 5, 5, 35, 70, 35, 5, 5, 60, 210, 210, 60, 5, 5, 90, 486, 840, 486, 90, 5, 5, 125, 960, 2550, 2550, 960, 125, 5, 5, 165, 1705, 6435, 9900, 6435, 1705, 165, 5, 5, 210, 2805, 14245, 31185, 31185, 14245, 2805, 210, 5
OFFSET
3,1
EXAMPLE
Triangle begins:
5, 0, 5;
5, 15, 15, 5;
5, 35, 70, 35, 5;
5, 60, 210, 210, 60, 5;
5, 90, 486, 840, 486, 90, 5;
5, 125, 960, 2550, 2550, 960, 125, 5;
5, 165, 1705, 6435, 9900, 6435, 1705, 165, 5;
5, 210, 2805, 14245, 31185, 31185, 14245, 2805, 210, 5;
...
MATHEMATICA
With[{k = 2}, Table[(((2 k + 1)/(m + k + 1))*Binomial[n - 1 - k, m - k] * Binomial[n + k, m + k] + ((2 k + 1)/(n - m + k))*Binomial[n - 1 - k, n - m - 1 - k] * Binomial[n + k, n - m - 1 + k]), {n, k + 1, 10}, {m, 0, n - 1}]] // Flatten (* Michael De Vlieger, Dec 19 2022 *)
CROSSREFS
Cf. A156715.
Sequence in context: A091672 A144702 A238192 * A055510 A200397 A265302
KEYWORD
nonn,tabf,less
AUTHOR
Roger L. Bagula, Feb 14 2009
STATUS
approved