A193895 -id:A193895

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A193896

Mirror of the triangle A193895.

+20
2

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

(list; table; graph; refs; listen; history; text; internal format)

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....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.

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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