A193974 Mirror of the triangle A193973.

2, 5, 3, 9, 7, 4, 14, 12, 9, 5, 20, 18, 15, 11, 6, 27, 25, 22, 18, 13, 7, 35, 33, 30, 26, 21, 15, 8, 44, 42, 39, 35, 30, 24, 17, 9, 54, 52, 49, 45, 40, 34, 27, 19, 10, 65, 63, 60, 56, 51, 45, 38, 30, 21, 11, 77, 75, 72, 68, 63, 57, 50, 42, 33, 23, 12, 90, 88, 85, 81

Offset

0,1

Comments

A193974 is obtained by reversing the rows of the triangle A193973.

Links

Table of n, a(n) for n=0..69.

Formula

Write w(n,k) for the triangle at A193973. The triangle at A193974 is then given by w(n,n-k).

Example

First six rows:
2
5....3
9....7....4
14...12...9....5
20...18...15...11...6
27...25...22...18...13...7

Mathematica

z = 13;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[0, x_] := 1; q[n_, x_] := x*q[n - 1, x] + 1;
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}]]  (* A193973 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193974 *)

Crossrefs

Cf. A193973.

Sequence in context: A363677 A340927 A182480 * A319499 A318578 A119435

Adjacent sequences: A193971 A193972 A193973 * A193975 A193976 A193977

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved