A080382 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.

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, 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, 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

Offset: 1

Author

Labos Elemer, Mar 12 2003

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   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,  1,  1,  5,  5, 35;
		

Crossrefs

Cf. A007318, A001405, A080381.

Programs

Mathematica

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