A193892 Mirror of the triangle A193891.

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.

Links

Table of n, a(n) for n=0..63.

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

Adjacent sequences: A193889 A193890 A193891 * A193893 A193894 A193895

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved