A174712 Triangle T(n,k) read by rows in which the right border is A000041, else zero, n >= 0.

1, 0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77

Offset: 0

Author

Gary W. Adamson, Mar 27 2010

Keywords

• nonn
• tabl

Comments

Eigensequence of the triangle = A058694: (1, 1, 2, 6, 30, 210,...), i.e., given A058694 preceded by a "1", triangle A174712 * the latter variant = the same sequence but shifted left.

Examples

			Triangle begins:
  1;
  0, 1;
  0, 0, 2;
  0, 0, 0, 3;
  0, 0, 0, 0, 5;
  0, 0, 0, 0, 0, 7;
  0, 0, 0, 0, 0, 0, 11;
  0, 0, 0, 0, 0, 0, 0, 15;
  0, 0, 0, 0, 0, 0, 0, 0, 22;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 30;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).

Crossrefs

Cf. A000041, A058694, A174713, A174714, A174715.

Programs

Mathematica

Array[PadLeft[{PartitionsP[#-1]}, #] &, 15] (* Paolo Xausa, Feb 21 2024 *)

Extensions

Definition clarified by Omar E. Pol, Feb 21 2024