A193898 Mirror of the triangle A193897.

1, 1, 2, 3, 6, 3, 6, 12, 9, 4, 10, 20, 18, 12, 5, 15, 30, 30, 24, 15, 6, 21, 42, 45, 40, 30, 18, 7, 28, 56, 63, 60, 50, 36, 21, 8, 36, 72, 84, 84, 75, 60, 42, 24, 9, 45, 90, 108, 112, 105, 90, 70, 48, 27, 10, 55, 110, 135, 144, 140, 126, 105, 80, 54, 30, 11, 66, 132

Offset

0,3

Comments

A193898 is obtained by reversing the rows of the triangle A193897.

Links

Table of n, a(n) for n=0..67.

Formula

Write w(n,k) for the triangle at A193897. The triangle at A193898 is then given by w(n,n-k).

Example

First six rows:
1
1....2
3....6....3
6....12...9....4
10...20...18...12...5
15...30...30...24...15...6

Mathematica

z = 12;
p[n_, x_] := (n + 1)*x^n + p[n - 1, x] (* #7 *); p[0, x_] := 1;
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}]]  (* A193897 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193898 *)

Crossrefs

Cf. A193897.

Sequence in context: A275733 A245499 A323642 * A129915 A019773 A350728

Adjacent sequences: A193895 A193896 A193897 * A193899 A193900 A193901

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved