A382448 Triangle read by rows, defined by the two-variable g.f. (x^3*y^2 + x^3*y + 1)/(1 - x^2*y - x*y - x).

1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 8, 15, 8, 1, 1, 10, 29, 29, 10, 1, 1, 12, 47, 73, 47, 12, 1, 1, 14, 69, 149, 149, 69, 14, 1, 1, 16, 95, 265, 371, 265, 95, 16, 1, 1, 18, 125, 429, 785, 785, 429, 125, 18, 1, 1, 20, 159, 649, 1479, 1941, 1479, 649, 159, 20, 1

Offset: 0

Author

F. Chapoton, Mar 26 2025

Keywords

• nonn
• tabl

Comments

Every row is symmetric.

Examples

			Triangle begins:
  [0] [1]
  [1] [1,  1]
  [2] [1,  3,   1]
  [3] [1,  6,   6,   1]
  [4] [1,  8,  15,   8,   1]
  [5] [1, 10,  29,  29,  10,  1]
  [6] [1, 12,  47,  73,  47, 12,    1]
  [7] [1, 14,  69, 149, 149, 69,   14,   1]
  [8] [1, 16,  95, 265, 371, 265,  95,  16, 1]
  [9] [1, 18, 125, 429, 785, 785, 429, 125, 18, 1]
		

Crossrefs

Similar to A008288, A103450, A382436 and A382444. Row sums are A105082.

Programs

Sage

y = polygen(QQ, 'y')
x = y.parent()[['x']].gen()
gf = (x^3*y^2 + x^3*y + 1)/(1 - x^2*y - x*y - x)
[list(u) for u in list(gf.O(10))]