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A193847 Mirror of the triangle A193846. 4
2, 8, 4, 26, 28, 8, 80, 136, 80, 16, 242, 568, 512, 208, 32, 728, 2188, 2672, 1648, 512, 64, 2186, 8020, 12392, 10288, 4832, 1216, 128, 6560, 28432, 53216, 55648, 35072, 13312, 2816, 256, 19682, 98416, 216512, 273376, 216512, 110080, 35072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A193847 is obtained by reversing the rows of the triangle A193846.

LINKS

Table of n, a(n) for n=0..42.

FORMULA

Write w(n,k) for the triangle at A193846.  The triangle at A193847 is then given by w(n,n-k).

EXAMPLE

First six rows:

2

8.....4

26....28....8

80....136...80....16

242...568...512...208...32

728...2188..2672..1648..512..64

MATHEMATICA

p[n_, x_] := (x + 2)^n;

q[n_, x_] := (x + 1)^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}]]   (* A193846 *)

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

Flatten[Table[h[n], {n, -1, z}]]  (* A193847 *)

TableForm[Table[Reverse[h[n]/2], {n, 0, z}]]

Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193848 *)

TableForm[Table[h[n]/2, {n, 0, z}]]

Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193849 *)

CROSSREFS

Cf. A193846, A193849.

Sequence in context: A054788 A193851 A276624 * A019194 A038214 A195923

Adjacent sequences:  A193844 A193845 A193846 * A193848 A193849 A193850

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 07 2011

STATUS

approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)