A193847 - OEIS

A193847

Mirror of the triangle A193846.

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

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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:

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