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

0,4

Comments

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

Links

Table of n, a(n) for n=0..69.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A193740.

Sequence in context: A284554 A078033 A221712 * A193824 A108075 A215120

Adjacent sequences: A193738 A193739 A193740 * A193742 A193743 A193744

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 04 2011

Status

approved