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A193896
Mirror of the triangle A193895.
2
1, 1, 2, 3, 6, 6, 6, 12, 15, 12, 10, 20, 27, 28, 20, 15, 30, 42, 48, 45, 30, 21, 42, 60, 72, 75, 66, 42, 28, 56, 81, 100, 110, 108, 91, 56, 36, 72, 105, 132, 150, 156, 147, 120, 72, 45, 90, 132, 168, 195, 210, 210, 192, 153, 90, 55, 110, 162, 208, 245, 270, 280
OFFSET
0,3
COMMENTS
A193896 is obtained by reversing the rows of the triangle A193895.
FORMULA
Write w(n,k) for the triangle at A193895. The triangle at A193896 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....2
3....6....6
6....12...15...12
10...20...27...28...20
15...30...42...48...45...30
MATHEMATICA
z = 9;
p[n_, x_] := x*p[n - 1, x] + n + 1 (* #6 *) ; p[0, x_] := 1;
q[n_, x_] := (n + 1)*x^n + q[n - 1, x] (* #7 *); q[0, x_] := 1;
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}]] (* A193895 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193896 *)
CROSSREFS
Cf. A193895.
Sequence in context: A078706 A077082 A333936 * A099162 A187327 A271716
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved