A193741 Mirror of the triangle A193740.

1, 1, 1, 3, 3, 1, 9, 9, 4, 1, 19, 19, 10, 4, 1, 34, 34, 20, 10, 4, 1, 55, 55, 35, 20, 10, 4, 1, 83, 83, 56, 35, 20, 10, 4, 1, 119, 119, 84, 56, 35, 20, 10, 4, 1, 164, 164, 120, 84, 56, 35, 20, 10, 4, 1, 219, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1, 285, 285, 220, 165

Offset: 0

Author

Clark Kimberling, Aug 04 2011

Keywords

• nonn
• tabl

Comments

A193741 is obtained by reversing the rows of the triangle A193740.

Examples

			First six rows:
1
1....1
3....3....1
9....9....4....1
19...19...10...4...1
34...34...20...10..4..1
		

Crossrefs

Cf. A193740.

Programs

Mathematica

z = 12;
p[0, x_] := 1
p[n_, x_] := n + Sum[(k + 1) x^(n - k), {k, 0, n - 1}]
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
t[n_, n_] := 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}]]  (* A193740 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]   (* A193741 *)

Formula

Write w(n,k) for the triangle at A193740. The triangle at A193741 is then given by w(n,n-k).