A080382 - OEIS

%I #11 Oct 27 2019 05:17:00

%S 1,1,1,2,1,2,3,1,1,3,6,3,1,3,6,10,2,1,1,2,10,20,10,4,1,4,10,20,35,5,5,

%T 1,1,5,5,35,70,35,5,5,1,5,5,35,70,126,14,7,3,1,1,3,7,14,126,252,126,

%U 28,21,6,1,6,21,28,126,252,462,42,42,14,7,1,1,7,14,42,42,462,924,77,14,21,28

%N Triangle read by rows: T(n,k) = C(n,floor(n/2))/gcd(C(n,floor(n/2)),C(n,k)), k=0..n; central binomial coefficient is divided by greatest common divisor of binomial coefficients and corresponding central binomial coefficient.

%e Triangle begins:

%e    1;

%e    1,  1;

%e    2,  1,  2;

%e    3,  1,  1,  3;

%e    6,  3,  1,  3,  6;

%e   10,  2,  1,  1,  2, 10;

%e   20, 10,  4,  1,  4, 10, 20;

%e   35,  5,  5,  1,  1,  5,  5, 35;

%t Table[Table[Binomial[n, Floor[n/2]]/GCD[Binomial[n, j], Binomial[n, Floor[n/2]]], {j, 0, n}], {n, 1, 10}]

%Y Cf. A007318, A001405, A080381.

%K nonn,tabl

%O 1,4

%A _Labos Elemer_, Mar 12 2003