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A328901
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Triangle T(n, k) read by rows: T(n, k) is the numerator of the rational Catalan number defined as binomial(n + k, n)/(n + k) for n > 0 and T(0, 0) = 1.
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3
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1, 1, 1, 1, 1, 3, 1, 1, 2, 10, 1, 1, 5, 5, 35, 1, 1, 3, 7, 14, 126, 1, 1, 7, 28, 21, 42, 77, 1, 1, 4, 12, 30, 66, 132, 1716, 1, 1, 9, 15, 165, 99, 429, 429, 6435, 1, 1, 5, 55, 55, 143, 1001, 715, 1430, 24310, 1, 1, 11, 22, 143, 1001, 1001, 1144, 2431, 4862, 46189, 1, 1, 6, 26, 91, 273, 728, 1768, 3978, 8398, 16796, 352716
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OFFSET
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0,6
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LINKS
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FORMULA
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T(n, k) = lcm(binomial(n + k, n), n + k)/(n + k) for n > 0.
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EXAMPLE
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n\k| 0 1 2 3 4 5 6
---+----------------------------
0 | 1
1 | 1 1
2 | 1 1 3
3 | 1 1 2 10
4 | 1 1 5 5 35
5 | 1 1 3 7 14 126
6 | 1 1 7 28 21 42 77
...
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MATHEMATICA
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Flatten[Join[{1}, Table[LCM[Binomial[n+k, n], n+k]/(n+k), {n, 1, 11}, {k, 0, n}]]]
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CROSSREFS
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Main diagonal gives A201058 (for n>0).
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KEYWORD
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AUTHOR
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STATUS
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approved
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