

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
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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,nk).


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



