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A193822 Mirror of the triangle A193821. 4
1, 1, 1, 3, 3, 2, 9, 9, 8, 4, 27, 27, 26, 20, 8, 81, 81, 80, 72, 48, 16, 243, 243, 242, 232, 192, 112, 32, 729, 729, 728, 716, 656, 496, 256, 64, 2187, 2187, 2186, 2172, 2088, 1808, 1248, 576, 128, 6561, 6561, 6560, 6544, 6432, 5984, 4864, 3072, 1280, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A193822 is obtained by reversing the rows of the triangle A193821.
LINKS
FORMULA
Write w(n,k) for the triangle at A193821. The triangle at A193822 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
3....3....2
9....9....8.....4
27...27...26....20...8
81...81...80....72...48...16
MATHEMATICA
p[n_, x_] := (a*x + b)^n
q[0, x_] := 1
q[n_, x_] := x*q[n - 1, x] + 1; q[n_, 0] := q[n, x] /. x -> 0;
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}]] (* A193821 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193822 *)
CROSSREFS
Sequence in context: A286952 A100052 A128504 * A202699 A058137 A250304
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 06 2011
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)