A082905 - OEIS

%I #13 Aug 30 2019 22:05:35

%S 1,1,1,1,2,1,1,3,3,1,1,4,2,4,1,1,5,10,10,5,1,1,6,3,2,3,6,1,1,7,21,35,

%T 35,21,7,1,1,8,4,56,2,56,4,8,1,1,9,36,3,126,126,3,36,9,1,1,10,5,120,

%U 10,2,10,120,5,10,1,1,11,55,165,330,462,462,330,165,55,11,1,1,12,6,4,3,792,2,792,3,4,6,12,1

%N Modified Pascal-triangle, read by rows. All C(n,j) binomial coefficients are replaced by C(n/g, j/g), where g = gcd(n,j).

%H G. C. Greubel, <a href="/A082905/b082905.txt">Rows n = 0..100 of triangle, flattened</a>

%e Triangle begins:

%e   1;

%e   1,  1;

%e   1,  2,  1;

%e   1,  3,  3,   1;

%e   1,  4,  2,   4,   1;

%e   1,  5, 10,  10,   5,   1;

%e   1,  6,  3,   2,   3,   6,  1;

%e   1,  7, 21,  35,  35,  21,  7,   1;

%e   1,  8,  4,  56,   2,  56,  4,   8, 1;

%e   1,  9, 36,   3, 126, 126,  3,  36, 9,  1;

%e   1, 10,  5, 120,  10,   2, 10, 120, 5, 10, 1;

%t Flatten[Table[Table[Binomial[n/GCD[n, j], j/GCD[n, j]], {j, 0, n}], {n, 1, 32}], 1]

%o (PARI) T(n,k) = my(g=gcd(n,k)); if (!g, g=1); binomial(n/g, k/g);

%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", "))); \\ _Michel Marcus_, Aug 30 2019

%o (Sage)

%o def T(n,k):

%o     if k==0 or k==n: return 1

%o     else: return binomial(n/gcd(n,k), k/gcd(n,k))

%o [[T(n,k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Aug 30 2019

%o (GAP)

%o T:= function(n,k)

%o     if k=0 or k=n then return 1;

%o     else return Binomial(n/Gcd(n,k), k/Gcd(n,k));

%o     fi;

%o   end;

%o Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Aug 30 2019

%Y Cf. A000005, A007318, A056045.

%K nonn,tabl

%O 0,5

%A _Labos Elemer_, Apr 23 2003

%E More terms from _Michel Marcus_, Aug 30 2019