A094496 Triangle read by rows: T(n,k) = binomial(n,k) - binomial(n,k) mod n^2, with T(0,0) = 1.

1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 81, 81, 81, 81, 0, 0, 0, 0, 0, 0, 100, 200, 200, 200, 100, 0, 0, 0, 0, 0, 0, 121, 242, 363, 363, 242, 121, 0, 0, 0, 0, 0, 0, 144, 432, 720, 864, 720, 432, 144, 0, 0, 0

Offset: 0

Author

Labos Elemer, Jun 02 2004

Keywords

• easy
• nonn
• tabl
• less

Examples

			Triangle begins:
  1;
  1, 1;
  0, 0, 0;
  0, 0, 0,   0;
  0, 0, 0,   0,   0;
  0, 0, 0,   0,   0,   0;
  0, 0, 0,   0,   0,   0,   0;
  0, 0, 0,   0,   0,   0,   0,   0;
  0, 0, 0,   0,  64,   0,   0,   0, 0;
  0, 0, 0,  81,  81,  81,  81,   0, 0, 0;
  0, 0, 0, 100, 200, 200, 200, 100, 0, 0, 0;
  ...
T(8,6) = binomial(8,4) - binomial(8,4) mod 8^2 = 70 - 6 = 64.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Crossrefs

Cf. A007318, A053200, A094495, A094497.

Programs

Mathematica

Flatten[Table[Table[Binomial[n, j]-Mod[Binomial[n, j], n^2], {j, 0, n}], {n, 1, 20}], 1]

PARI

T(n,k) = my(x=binomial(n,k)); x - if(n, x % n^2) \\ Andrew Howroyd, Dec 12 2024

Formula

T(n,k) = A007318(n,k) - A094495(n,k).