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

0,2

Comments

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

Links

Table of n, a(n) for n=0..48.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A193858.

Sequence in context: A348535 A018891 A034423 * A174330 A099329 A182871

Adjacent sequences: A193856 A193857 A193858 * A193860 A193861 A193862

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 07 2011

Status

approved