A291960 Triangle read by rows: T(n,k) = T(n-k,k-1) + k * T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 3, 0, 1, 3, 1, 0, 1, 7, 1, 0, 1, 7, 3, 0, 1, 15, 6, 0, 1, 15, 10, 1, 0, 1, 31, 16, 1, 0, 1, 31, 33, 3, 0, 1, 63, 45, 6, 0, 1, 63, 79, 14, 0, 1, 127, 130, 20, 1, 0, 1, 127, 198, 45, 1, 0, 1, 255, 300, 69, 3, 0, 1, 255, 517, 135

Offset: 0

Author

Seiichi Manyama, Sep 06 2017

Keywords

• nonn
• tabf

Examples

			First few rows are:
  1;
  0, 1;
  0, 1;
  0, 1,  1;
  0, 1,  1;
  0, 1,  3;
  0, 1,  3,  1;
  0, 1,  7,  1;
  0, 1,  7,  3;
  0, 1, 15,  6;
  0, 1, 15, 10, 1.
		

Links

• Seiichi Manyama, Rows n = 0..481, flattened

Crossrefs

Row sums give A204856.

Columns 0-2 give A000007, A000012, A052551(n-3).

Cf. A008289, A216652, A291969.

Formula

G.f. of column k: x^(k*(k+1)/2) / Product_{j=1..k} (1-j*x^j).