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A328901 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.

%I A328901 #16 Oct 30 2020 12:19:36
%S A328901 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,
%T A328901 4,12,30,66,132,1716,1,1,9,15,165,99,429,429,6435,1,1,5,55,55,143,
%U A328901 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
%N A328901 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.
%H A328901 Stefano Spezia, <a href="/A328901/b328901.txt">First 141 rows of the triangle, flattened</a>
%H A328901 D. Armstrong, N. A. Loehr, G. S. Warrington, <a href="https://doi.org/10.1007/s00026-015-0293-6">Rational Parking Functions and Catalan Numbers</a>, Annals of Combinatorics (2016), Volume 20, Issue 1, pp 21-58.
%H A328901 M. T. L. Bizley, <a href="http://bergeron.math.uqam.ca/wp-content/uploads/2014/09/Bizley.pdf">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</a>, Journal of the Institute of Actuaries, Vol. 80, No. 1 (1954): 55-62.
%F A328901 T(n, k) = lcm(binomial(n + k, n), n + k)/(n + k) for n > 0.
%e A328901 n\k|   0   1   2   3   4   5   6
%e A328901 ---+----------------------------
%e A328901 0  |   1
%e A328901 1  |   1   1
%e A328901 2  |   1   1   3
%e A328901 3  |   1   1   2  10
%e A328901 4  |   1   1   5   5  35
%e A328901 5  |   1   1   3   7  14 126
%e A328901 6  |   1   1   7  28  21  42  77
%e A328901 ...
%t A328901 Flatten[Join[{1},Table[LCM[Binomial[n+k,n],n+k]/(n+k),{n,1,11},{k,0,n}]]]
%Y A328901 Main diagonal gives A201058 (for n>0).
%Y A328901 Cf. A000108, A046899, A051162, A328902 (denominator).
%K A328901 frac,nonn,tabl
%O A328901 0,6
%A A328901 _Stefano Spezia_, Oct 30 2019