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A193898
Mirror of the triangle A193897.
2
1, 1, 2, 3, 6, 3, 6, 12, 9, 4, 10, 20, 18, 12, 5, 15, 30, 30, 24, 15, 6, 21, 42, 45, 40, 30, 18, 7, 28, 56, 63, 60, 50, 36, 21, 8, 36, 72, 84, 84, 75, 60, 42, 24, 9, 45, 90, 108, 112, 105, 90, 70, 48, 27, 10, 55, 110, 135, 144, 140, 126, 105, 80, 54, 30, 11, 66, 132
OFFSET
0,3
COMMENTS
A193898 is obtained by reversing the rows of the triangle A193897.
FORMULA
Write w(n,k) for the triangle at A193897. The triangle at A193898 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....2
3....6....3
6....12...9....4
10...20...18...12...5
15...30...30...24...15...6
MATHEMATICA
z = 12;
p[n_, x_] := (n + 1)*x^n + p[n - 1, x] (* #7 *); p[0, x_] := 1;
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}]] (* A193897 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193898 *)
CROSSREFS
Cf. A193897.
Sequence in context: A275733 A245499 A323642 * A129915 A019773 A350728
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved