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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
A193964 is obtained by reversing the rows of the triangle A193963.
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
Cf. A193963.
Sequence in context: A346060 A041255 A042835 * A337443 A099897 A050251
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)