A193980 Mirror of the triangle A193979.

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

Offset

0,2

Comments

A193980 is obtained by reversing the rows of the triangle A193977.

Links

Table of n, a(n) for n=0..65.

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

Adjacent sequences: A193977 A193978 A193979 * A193981 A193982 A193983

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved