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A193741
Mirror of the triangle A193740.
3
1, 1, 1, 3, 3, 1, 9, 9, 4, 1, 19, 19, 10, 4, 1, 34, 34, 20, 10, 4, 1, 55, 55, 35, 20, 10, 4, 1, 83, 83, 56, 35, 20, 10, 4, 1, 119, 119, 84, 56, 35, 20, 10, 4, 1, 164, 164, 120, 84, 56, 35, 20, 10, 4, 1, 219, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1, 285, 285, 220, 165
OFFSET
0,4
COMMENTS
A193741 is obtained by reversing the rows of the triangle A193740.
FORMULA
Write w(n,k) for the triangle at A193740. The triangle at A193741 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....1
3....3....1
9....9....4....1
19...19...10...4...1
34...34...20...10..4..1
MATHEMATICA
z = 12;
p[0, x_] := 1
p[n_, x_] := n + Sum[(k + 1) x^(n - k), {k, 0, n - 1}]
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
t[n_, n_] := 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}]] (* A193740 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193741 *)
CROSSREFS
Cf. A193740.
Sequence in context: A284554 A078033 A221712 * A193824 A108075 A215120
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 04 2011
STATUS
approved