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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
A193972 is obtained by reversing the rows of the triangle A193971.
LINKS
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

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)