|
|
A193964
|
|
Mirror of the triangle A193963.
|
|
2
|
|
|
1, 1, 4, 5, 20, 9, 14, 56, 45, 16, 30, 120, 126, 80, 25, 55, 220, 270, 224, 125, 36, 91, 364, 495, 480, 350, 180, 49, 140, 560, 819, 880, 750, 504, 245, 64, 204, 816, 1260, 1456, 1375, 1080, 686, 320, 81, 285, 1140, 1836, 2240, 2275, 1980, 1470, 896
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Write w(n,k) for the triangle at A193963. The triangle at A193964 is then given by w(n,n-k).
|
|
EXAMPLE
|
First six rows:
1
1....4
5....20....9
14...56....45....16
30...120...126...80....25
55...220...270...224...125...36
|
|
MATHEMATICA
|
p[n_, x_] := Sum[((k + 1)^2)*x^k, {k, 0, n}]
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}]] (* A193963 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193964 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|