OFFSET
1,2
COMMENTS
An LCM-analog of the binomial coefficients. - N. J. A. Sloane, Aug 26 2015
LINKS
Bakir Farhi, An analog of the arithmetic triangle obtained by replacing the products by the least common multiples, arXiv:1002.1383 [math.NT], 2010.
Siao Hong and Guoyou Qian, On the lcm-analog of binomial coefficient, Asian-European Journal of Mathematics, Volume 07, Issue 04, December 2014; DOI: 10.1142/S1793557114500569.
EXAMPLE
T(7,3) = lcm(7,6,5)/lcm(1,2,3) = 210/6 = 35.
Triangle starts:
1;
2, 1;
3, 3, 1;
4, 6, 2, 1;
5, 10, 10, 5, 1;
6, 15, 10, 5, 1, 1;
...
MAPLE
T:=(n, k)->lcm(seq(i, i=n-k+1..n))/lcm(seq(j, j=1..k)): for n from 1 to 13 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form # Emeric Deutsch, Jan 30 2006
MATHEMATICA
t[n_, k_] := LCM @@ Table[j, {j, n-k+1, n}] / LCM @@ Table[j, {j, 1, k}]; t[_, 0] = 1; Table[t[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 23 2014 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Mar 31 2004
EXTENSIONS
More terms from Emeric Deutsch, Jan 30 2006
STATUS
approved