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A193892 Mirror of the triangle A193891. 2
1, 2, 1, 8, 5, 2, 20, 14, 8, 3, 40, 30, 20, 11, 4, 70, 55, 40, 26, 14, 5, 112, 91, 70, 50, 32, 17, 6, 168, 140, 112, 85, 60, 38, 20, 7, 240, 204, 168, 133, 100, 70, 44, 23, 8, 330, 285, 240, 196, 154, 115, 80, 50, 26, 9, 440, 385, 330, 276, 224, 175, 130, 90, 56 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A193892 is obtained by reversing the rows of the triangle A193891.

LINKS

Table of n, a(n) for n=0..63.

FORMULA

Write w(n,k) for the triangle at A193891.  The triangle at A193892 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

2....1

8....5....2

20...14...8....3

40...30...20...11...4

70...55...40...26...14...5

MATHEMATICA

z = 9;

p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 1;

q[n_, x_] := p[n, x];

t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

g[n_] := CoefficientList[w[n, x], {x}]

TableForm[Table[Reverse[g[n]], {n, -1, z}]]

Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193891 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]]  (* A193892 *)

CROSSREFS

Cf. A193891.

Sequence in context: A245836 A135520 A136230 * A193907 A298592 A344163

Adjacent sequences:  A193889 A193890 A193891 * A193893 A193894 A193895

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)