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A328902
Triangle T(n, k) read by rows: T(n, k) is the denominator of the rational Catalan number defined as binomial(n + k, n)/(n + k) for 0 <= k <= n, n > 0; T(0, 0) = 1.
3
1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 4, 1, 2, 1, 4, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 8, 1, 2, 1, 4, 1, 2, 1, 8, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 10, 1, 2, 1, 2, 5, 2, 1, 1, 1, 5, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 12, 1, 2, 3, 4, 1, 3, 1, 2, 3, 1, 1, 6
OFFSET
0,4
FORMULA
T(n, k) = (n + k)/gcd(binomial(n + k, n), n + k) for n > 0.
EXAMPLE
n\k| 0 1 2 3 4 5 6
---+--------------
0 | 1
1 | 1 1
2 | 2 1 2
3 | 3 1 1 3
4 | 4 1 2 1 4
5 | 5 1 1 1 1 5
6 | 6 1 2 3 1 1 1
...
MATHEMATICA
Flatten[Join[{1}, Table[(n+k)/GCD[n+k, Binomial[n+k, n]], {n, 1, 12}, {k, 0, n}]]]
PROG
(PARI) A328902(n, k)=if(n, (n+k)/gcd(binomial(n+k, n), n+k), 1) \\ M. F. Hasler, Nov 04 2019
CROSSREFS
Cf. A000108, A028310 (1st column), A046899, A051162, A328901 (numerator).
Sequence in context: A233864 A133232 A137152 * A159335 A109004 A103823
KEYWORD
frac,nonn,tabl
AUTHOR
Stefano Spezia, Oct 30 2019
STATUS
approved