A193859 Mirror of the triangle A193858.

1, 3, 2, 7, 10, 4, 15, 34, 28, 8, 31, 98, 124, 72, 16, 63, 258, 444, 392, 176, 32, 127, 642, 1404, 1672, 1136, 416, 64, 255, 1538, 4092, 6152, 5616, 3104, 960, 128, 511, 3586, 11260, 20488, 23536, 17440, 8128, 2176, 256, 1023, 8194, 29692, 63496

Offset: 0

Author

Clark Kimberling, Aug 07 2011

Keywords

• nonn
• tabl

Comments

A193859 is obtained by reversing the rows of the triangle A193858.

Examples

			First six rows:
1
3....2
7....10...4
15...34...28...8
31...98...124..72...16
63...258..444..392..176..32
		

Crossrefs

Cf. A193858.

Programs

Mathematica

z = 10;
p[n_, x_] := (x + 1)^n;
q[n_, x_] := (2 x + 1)^n;
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193858 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]   (* A193859 *)

Formula

Write w(n,k) for the triangle at A193858. The triangle at A193859 is then given by w(n,n-k).