A055894 Inverse Moebius transform of Pascal's triangle A007318.

1, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 4, 8, 4, 3, 2, 5, 10, 10, 5, 2, 4, 6, 18, 22, 18, 6, 4, 2, 7, 21, 35, 35, 21, 7, 2, 4, 8, 32, 56, 78, 56, 32, 8, 4, 3, 9, 36, 87, 126, 126, 87, 36, 9, 3, 4, 10, 50, 120, 220, 254, 220, 120, 50, 10, 4, 2, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11

Offset: 0

Author

Christian G. Bower, Jun 09 2000

Keywords

• nonn
• tabl

Examples

			Triangle starts:
  [0]  1;
  [1]  1,   1;
  [2]  2,   2,   2;
  [3]  2,   3,   3,   2;
  [4]  3,   4,   8,   4,   3;
  [5]  2,   5,  10,  10,   5,   2;
  [6]  4,   6,  18,  22,  18,   6,   4;
  [7]  2,   7,  21,  35,  35,  21,   7,   2;
  [8]  4,   8,  32,  56,  78,  56,  32,   8,   4;
  [9]  3,   9,  36,  87, 126, 126,  87,  36,   9,   3;
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 101 rows, flattened
• N. J. A. Sloane, Transforms
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A007318.

Row sums give A055895.

Programs

Mathematica

T[n_, k_] := DivisorSum[GCD[k, n], Binomial[n/#, k/#] &]; T[0, 0] = 1; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 02 2015 *)

PARI

T(n,k) = if(n<=0, n==0, sumdiv(gcd(n,k), d, binomial(n/d,k/d) ) );
/* print triangle: */
{ for (n=0, 17, for (k=0, n, print1(T(n,k),", "); ); print(); ); }
/* Joerg Arndt, Oct 21 2012 */