A193976 Mirror of the triangle A193975.

2, 8, 3, 20, 11, 4, 40, 26, 14, 5, 70, 50, 32, 17, 6, 112, 85, 60, 38, 20, 7, 168, 133, 100, 70, 44, 23, 8, 240, 196, 154, 115, 80, 50, 26, 9, 330, 276, 224, 175, 130, 90, 56, 29, 10, 440, 375, 312, 252, 196, 145, 100, 62, 32, 11, 572, 495, 420, 348, 280, 217

Offset: 0

Author

Clark Kimberling, Aug 10 2011

Keywords

• nonn
• tabl

Comments

A193976 is obtained by reversing the rows of the triangle A193975.

Examples

			First six rows:
2
8.....3
20....11...4
40....26...14...5
70....50...32...17...6
112...85...60...38...20...7
		

Crossrefs

Cf. A193975.

Programs

Mathematica

z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[n_, x_] := p[n, x];
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193975 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193976 *)

Formula

Write w(n,k) for the triangle at A193975. The triangle at A193976 is then given by w(n,n-k).