A382880 Symmetric triangle read by rows refining A109113.

1, 1, 1, 6, 6, 1, 1, 11, 33, 33, 11, 1, 1, 16, 85, 189, 189, 85, 16, 1, 1, 21, 162, 590, 1107, 1107, 590, 162, 21, 1, 1, 26, 264, 1361, 3919, 6588, 6588, 3919, 1361, 264, 26, 1, 1, 31, 391, 2627, 10400, 25484, 39663, 39663, 25484, 10400, 2627, 391, 31, 1

Offset: 0

Author

F. Chapoton, Apr 07 2025

Keywords

• nonn
• tabf

Comments

Every row is symmetric. Alternating row sums vanish.

Examples

			Triangle begins:
  1,  1;
  1,  6,   6,   1;
  1, 11,  33,  33,   11,    1;
  1, 16,  85, 189,  189,   85,  16,   1;
  1, 21, 162, 590, 1107, 1107, 590, 162, 21, 1;
  ...
		

Crossrefs

Cf. A109113 (row sums).

Programs

Sage

y = polygen(QQ,'y')
t = LazyPowerSeriesRing(y.parent(),'t').gen()
v = (1+y)*(1+y*t)/(1-(1+4*y+y**2)*t-(y+y**2+y**3)*t**2)
[list(cf) for cf in v[:8]]

Formula

G.f.: (1+y)*(1+y*t)/(1-(1+4*y+y^2)*t-(y+y^2+y^3)*t^2).