A193962 Mirror of the triangle A193961.

1, 4, 1, 40, 17, 4, 184, 98, 40, 9, 584, 354, 184, 73, 16, 1484, 979, 584, 298, 116, 25, 3248, 2275, 1484, 874, 440, 169, 36, 6384, 4676, 3248, 2099, 1224, 610, 232, 49, 11568, 8772, 6384, 4403, 2824, 1634, 808, 305, 64, 19668, 15333, 11568, 8372

Offset

0,2

Comments

A193962 is obtained by reversing the rows of the triangle A193961.

Links

Table of n, a(n) for n=0..48.

Formula

Write w(n,k) for the triangle at A193961. The triangle at A193962 is then given by w(n,n-k).

Example

First six rows:
1
4......1
40.....17....4
184....98....40....9
584....354...184...73...16
1484...979...584...298..116..25

Mathematica

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*x^(n - k), {k, 0, n}]
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}]]  (* A193961 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193962 *)

Crossrefs

Cf. A193961.

Sequence in context: A297900 A363819 A298495 * A369868 A302441 A269906

Adjacent sequences: A193959 A193960 A193961 * A193963 A193964 A193965

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved