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

0,5

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

Links

Table of n, a(n) for n=0..90.

Example

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

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}]]

Prog

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

Crossrefs

Cf. A007318, A001405.

Sequence in context: A343033 A307239 A204087 * A080396 A155582 A169946

Adjacent sequences: A080378 A080379 A080380 * A080382 A080383 A080384

Keyword

nonn,tabl

Author

Labos Elemer, Mar 12 2003

Extensions

More terms from Michel Marcus, Sep 03 2019

Status

approved