A193896 Mirror of the triangle A193895.

1, 1, 2, 3, 6, 6, 6, 12, 15, 12, 10, 20, 27, 28, 20, 15, 30, 42, 48, 45, 30, 21, 42, 60, 72, 75, 66, 42, 28, 56, 81, 100, 110, 108, 91, 56, 36, 72, 105, 132, 150, 156, 147, 120, 72, 45, 90, 132, 168, 195, 210, 210, 192, 153, 90, 55, 110, 162, 208, 245, 270, 280

Offset

0,3

Comments

A193896 is obtained by reversing the rows of the triangle A193895.

Links

Table of n, a(n) for n=0..61.

Formula

Write w(n,k) for the triangle at A193895. The triangle at A193896 is then given by w(n,n-k).

Example

First six rows:
1
1....2
3....6....6
6....12...15...12
10...20...27...28...20
15...30...42...48...45...30

Mathematica

z = 9;
p[n_, x_] := x*p[n - 1, x] + n + 1 (* #6 *)  ; p[0, x_] := 1;
q[n_, x_] := (n + 1)*x^n + q[n - 1, x] (* #7 *); q[0, x_] := 1;
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}]]  (* A193895 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193896 *)

Crossrefs

Cf. A193895.

Sequence in context: A078706 A077082 A333936 * A099162 A187327 A271716

Adjacent sequences: A193893 A193894 A193895 * A193897 A193898 A193899

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved