OFFSET
0,4
LINKS
Stefano Spezia, First 141 rows of the triangle, flattened
D. Armstrong, N. A. Loehr, G. S. Warrington, Rational Parking Functions and Catalan Numbers, Annals of Combinatorics (2016), Volume 20, Issue 1, pp 21-58.
M. T. L. Bizley, Derivation of a new formula for the number of minimal lattice paths from (0, 0) to (km, kn) having just t contacts with the line my = nx and having no points above this line; and a proof of Grossman's formula for the number of paths which may touch but do not rise above this line, Journal of the Institute of Actuaries, Vol. 80, No. 1 (1954): 55-62.
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
KEYWORD
AUTHOR
Stefano Spezia, Oct 30 2019
STATUS
approved