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A193892
Mirror of the triangle A193891.
2
1, 2, 1, 8, 5, 2, 20, 14, 8, 3, 40, 30, 20, 11, 4, 70, 55, 40, 26, 14, 5, 112, 91, 70, 50, 32, 17, 6, 168, 140, 112, 85, 60, 38, 20, 7, 240, 204, 168, 133, 100, 70, 44, 23, 8, 330, 285, 240, 196, 154, 115, 80, 50, 26, 9, 440, 385, 330, 276, 224, 175, 130, 90, 56
OFFSET
0,2
COMMENTS
A193892 is obtained by reversing the rows of the triangle A193891.
FORMULA
Write w(n,k) for the triangle at A193891. The triangle at A193892 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
2....1
8....5....2
20...14...8....3
40...30...20...11...4
70...55...40...26...14...5
MATHEMATICA
z = 9;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 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}]] (* A193891 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193892 *)
CROSSREFS
Cf. A193891.
Sequence in context: A368386 A135520 A136230 * A193907 A298592 A344163
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved