|
|
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
|
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|