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A193980 Mirror of the triangle A193979. 2
1, 3, 2, 9, 5, 3, 21, 13, 7, 4, 41, 28, 17, 9, 5, 71, 52, 35, 21, 11, 6, 113, 87, 63, 42, 25, 13, 7, 169, 135, 103, 74, 49, 29, 15, 8, 241, 198, 157, 119, 85, 56, 33, 17, 9, 331, 278, 227, 179, 135, 96, 63, 37, 19, 10, 441, 377, 315, 256, 201, 151, 107, 70, 41, 21, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A193980 is obtained by reversing the rows of the triangle A193977.
LINKS
FORMULA
Write w(n,k) for the triangle at A193979. The triangle at A193980 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
3....2
9....5....3
21...13...7....4
41...28...17...9....5
71...52...35...21...11...6
MATHEMATICA
z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n;
q[n_, x_] := p[n, x];
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}]] (* A193979 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]] (* A193980 *)
CROSSREFS
Cf. A193979.
Sequence in context: A258439 A346105 A188926 * A194001 A178230 A268824
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified May 21 21:53 EDT 2024. Contains 372738 sequences. (Running on oeis4.)