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A193962
Mirror of the triangle A193961.
2
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.
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: A363819 A298495 A373827 * A369868 A302441 A373459
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved