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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.
5
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
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
Sequence in context: A343033 A307239 A204087 * A080396 A155582 A169946
KEYWORD
nonn,tabl
AUTHOR
Labos Elemer, Mar 12 2003
EXTENSIONS
More terms from Michel Marcus, Sep 03 2019
STATUS
approved