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A193898 Mirror of the triangle A193897. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A109536

Adjacent sequences:  A193895 A193896 A193897 * A193899 A193900 A193901

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified October 26 07:47 EDT 2021. Contains 348262 sequences. (Running on oeis4.)