A193978 Mirror of the triangle A193977.

2, 5, 6, 9, 14, 12, 14, 24, 27, 20, 20, 36, 45, 44, 30, 27, 50, 66, 72, 65, 42, 35, 66, 90, 104, 105, 90, 56, 44, 84, 117, 140, 150, 144, 119, 72, 54, 104, 147, 180, 200, 204, 189, 152, 90, 65, 126, 180, 224, 255, 270, 266, 240, 189, 110, 77, 150, 216, 272

Offset

0,1

Comments

A193978 is obtained by reversing the rows of the triangle A193977.

Links

Table of n, a(n) for n=0..58.

Formula

Write w(n,k) for the triangle at A193977. The triangle at A193978 is then given by w(n,n-k).

Example

First six rows:
2
5....6
9....14...12
14...24...27...20
20...36...45...44...30
27...50...66...72...65...42

Mathematica

z = 11;
p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;
q[n_, x_] := Sum[(k + 1)*x^k, {k, 0, 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}]]  (* A193977 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193978 *)

Crossrefs

Cf. A193977.

Sequence in context: A255737 A366741 A271371 * A224486 A163782 A362140

Adjacent sequences: A193975 A193976 A193977 * A193979 A193980 A193981

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved