cp's OEIS Frontend

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.

%I A080381 #16 Jan 01 2024 13:21:13
%S A080381 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,
%T A080381 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,
%U A080381 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
%N 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.
%C A080381 The matrix inverse starts
%C A080381 1;
%C A080381 -1,1;
%C A080381 1,-2,1;
%C A080381 -1,3,-3,1;
%C A080381 -3,4,0,-2,1;
%C A080381 19,-35,20,0,-5,1;
%C A080381 -7,-2,15,-10,5,-2,1;
%C A080381 55,21,-147,105,-35,7,-7,1
%C A080381 -67,180,-168,56,0,0,0,-2,1; - _R. J. Mathar_, Mar 21 2013
%e A080381 Triangle begins:
%e A080381 1
%e A080381 1 1
%e A080381 1 2 1
%e A080381 1 3 3 1
%e A080381 1 2 6 2 1
%e A080381 1 5 10 10 5 1
%e A080381 1 2 5 20 5 2 1
%e A080381 1 7 7 35 35 7 7 1
%p A080381 A080381 := proc(n,k)
%p A080381     if k < 0 or k > n then
%p A080381         0;
%p A080381     else
%p A080381         igcd(binomial(n,floor(n/2)), binomial(n,k)) ;
%p A080381     end if;
%p A080381 end proc: # _R. J. Mathar_, Mar 21 2013
%t A080381 Flatten[Table[Table[GCD[Binomial[n, j], Binomial[n, Floor[n/2]]], {j, 0, n}], {n, 0, 10}]]
%o A080381 (PARI) T(n, k) = gcd(binomial(n, n\2), binomial(n, k)); \\ _Michel Marcus_, Sep 03 2019
%Y A080381 Cf. A007318, A001405.
%K A080381 nonn,tabl
%O A080381 0,5
%A A080381 _Labos Elemer_, Mar 12 2003
%E A080381 More terms from _Michel Marcus_, Sep 03 2019