A080381 Triangle read by rows: gcd(binomial(n,floor(n/2)), binomial(n,i)), i=0..n; greatest common divisor of binomial coefficients and corresponding central binomial coefficient.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 2, 5, 20, 5, 2, 1, 1, 7, 7, 35, 35, 7, 7, 1, 1, 2, 14, 14, 70, 14, 14, 2, 1, 1, 9, 18, 42, 126, 126, 42, 18, 9, 1, 1, 2, 9, 12, 42, 252, 42, 12, 9, 2, 1, 1, 11, 11, 33, 66, 462, 462, 66, 33, 11, 11, 1, 1, 12, 66, 44, 33, 132, 924, 132, 33, 44, 66, 12, 1

Offset: 0

Author

Labos Elemer, Mar 12 2003

Keywords

• nonn
• tabl

Comments

The matrix inverse starts

1;

-1,1;

1,-2,1;

-1,3,-3,1;

-3,4,0,-2,1;

19,-35,20,0,-5,1;

-7,-2,15,-10,5,-2,1;

55,21,-147,105,-35,7,-7,1

-67,180,-168,56,0,0,0,-2,1; - R. J. Mathar, Mar 21 2013

Examples

			Triangle begins:
1
1 1
1 2 1
1 3 3 1
1 2 6 2 1
1 5 10 10 5 1
1 2 5 20 5 2 1
1 7 7 35 35 7 7 1
		

Crossrefs

Cf. A007318, A001405.

Programs

Maple

A080381 := proc(n,k)
    if k < 0 or k > n then
        0;
    else
        igcd(binomial(n,floor(n/2)), binomial(n,k)) ;
    end if;
end proc: # R. J. Mathar, Mar 21 2013

Mathematica

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

PARI

T(n, k) = gcd(binomial(n, n\2), binomial(n, k)); \\ Michel Marcus, Sep 03 2019

Extensions

More terms from Michel Marcus, Sep 03 2019