A193894 Mirror of the triangle A193893.

1, 4, 2, 44, 28, 12, 210, 150, 90, 36, 680, 520, 360, 208, 80, 1750, 1400, 1050, 710, 400, 150, 3864, 3192, 2520, 1860, 1236, 684, 252, 7644, 6468, 5292, 4130, 3010, 1974, 1078, 392, 13920, 12000, 10080, 8176, 6320, 4560, 2960, 1600, 576, 23760

Offset

0,2

Comments

A193894 is obtained by reversing the rows of the triangle A193893.

Links

Table of n, a(n) for n=0..45.

Formula

Write w(n,k) for the triangle at A193893. The triangle at A193894 is then given by w(n,n-k).

Example

First six rows:
1
4.....2
44....28....12
210...150...90....36
680...520...360...208..80
1750..1400..1050..710..400..105

Mathematica

z = 9;
p[n_, x_] := Sum[(k + 1) (n + 1)*x^(n - k), {k, 0, n}]
q[n_, x_] := p[n, x];
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193893 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193894 *)

Crossrefs

Cf. A193893.

Sequence in context: A280780 A264755 A120968 * A107667 A362155 A163176

Adjacent sequences: A193891 A193892 A193893 * A193895 A193896 A193897

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved