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A193976 Mirror of the triangle A193975. 2
2, 8, 3, 20, 11, 4, 40, 26, 14, 5, 70, 50, 32, 17, 6, 112, 85, 60, 38, 20, 7, 168, 133, 100, 70, 44, 23, 8, 240, 196, 154, 115, 80, 50, 26, 9, 330, 276, 224, 175, 130, 90, 56, 29, 10, 440, 375, 312, 252, 196, 145, 100, 62, 32, 11, 572, 495, 420, 348, 280, 217 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193976 is obtained by reversing the rows of the triangle A193975.

LINKS

Table of n, a(n) for n=0..60.

FORMULA

Write w(n,k) for the triangle at A193975.  The triangle at A193976 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

8.....3

20....11...4

40....26...14...5

70....50...32...17...6

112...85...60...38...20...7

MATHEMATICA

z = 11;

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

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}]]  (* A193975 *)

TableForm[Table[h[n], {n, 0, z}]]

Flatten[Table[h[n], {n, -1, z}]]  (* A193976 *)

CROSSREFS

Cf. A193975.

Sequence in context: A083003 A278117 A153188 * A264244 A292930 A126951

Adjacent sequences:  A193973 A193974 A193975 * A193977 A193978 A193979

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified December 8 20:04 EST 2021. Contains 349596 sequences. (Running on oeis4.)