A193857 Mirror of the triangle A193856.

1, 5, 1, 19, 8, 1, 65, 43, 11, 1, 211, 194, 76, 14, 1, 665, 793, 422, 118, 17, 1, 2059, 3044, 2059, 776, 169, 20, 1, 6305, 11191, 9221, 4387, 1283, 229, 23, 1, 19171, 39878, 38854, 22382, 8236, 1970, 298, 26, 1, 58025, 138805, 156440, 106000, 47090

Offset

0,2

Comments

A193857 is obtained by reversing the rows of the triangle A193856.

Links

Table of n, a(n) for n=0..49.

Formula

Write w(n,k) for the triangle at A193856. The triangle at A193857 is then given by w(n,n-k).

Example

First six rows:
1
5.....1
19....8.....1
65....43....11....1
211...194...76....14....1
665...793...422...118...17...1

Mathematica

z = 10;
p[n_, x_] := (2 x + 1)^n;
q[n_, x_] := (x + 1)^n;
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}]]  (* A193856 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]   (* A193857 *)

Crossrefs

Cf. A193856.

Sequence in context: A055584 A193861 A349544 * A146055 A286232 A147437

Adjacent sequences: A193854 A193855 A193856 * A193858 A193859 A193860

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 07 2011

Status

approved