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A193972
Mirror of the triangle A193971.
2
2, 5, 3, 9, 11, 4, 14, 26, 19, 5, 20, 50, 55, 29, 6, 27, 85, 125, 99, 41, 7, 35, 133, 245, 259, 161, 55, 8, 44, 196, 434, 574, 476, 244, 71, 9, 54, 276, 714, 1134, 1176, 804, 351, 89, 10, 65, 375, 1110, 2058, 2562, 2190, 1275, 485, 109, 11, 77, 495, 1650
OFFSET
0,1
COMMENTS
A193972 is obtained by reversing the rows of the triangle A193971.
FORMULA
Write w(n,k) for the triangle at A193971. The triangle at A193972 is then given by w(n,n-k).
EXAMPLE
First six rows:
2
5....3
9....11...4
14...26...19....5
20...50...55....29...6
27...85...125...99...41...7
MATHEMATICA
z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
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}]] (* A193971 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193972 *)
CROSSREFS
Cf. A193971.
Sequence in context: A318578 A119435 A352783 * A361398 A332357 A305126
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved