|
|
A174986
|
|
Numerator coefficients of an infinite sum polynomial:p(x,n)=Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k* Sqrt[5]))^n*x^k, {k, 0, Infinity}]
|
|
0
|
|
|
-2, -1, 1, 5, -10, -5, -2, 8, 8, -2, -10, 70, 160, -70, -10, -1, 12, 53, -53, -12, 1, 20, -400, -3320, 6360, 3320, -400, -20, -2, 66, 984, -3568, -3568, 984, 66, -2, -10, 540, 14130, -92880, -178400, 92880, 14130, -540, -10, -4, 352, 15840, -184932, -654016
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Row sums are:
{-2, 0, -10, 12, 140, 0, 5560, -5040, -150160, 0,...}.
The result seems to be a beta integer version of a Eulerian infinite sum.
|
|
LINKS
|
|
|
FORMULA
|
p(x,n)=Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k* Sqrt[5]))^n*x^k, {k, 0, Infinity}] out_n,m=Numerator_coefficients(p(x,n)/x)/2^(1 + Floor[n/2])
|
|
EXAMPLE
|
{-2},
{-1, 1},
{5, -10, -5},
{-2, 8, 8, -2},
{-10, 70, 160, -70, -10},
{-1, 12, 53, -53, -12, 1},
{20, -400, -3320, 6360, 3320, -400, -20},
{-2, 66, 984, -3568, -3568, 984, 66, -2},
{-10, 540, 14130, -92880, -178400, 92880, 14130, -540, -10},
{-4, 352, 15840, -184932, -654016, 654016, 184932, -15840, -352, 4}
|
|
MATHEMATICA
|
p[x_, n_] = Sum[(((1 + Sqrt[5])^k - (1 - Sqrt[5])^k)/(2^k*Sqrt[5]))^n*x^k, {k, 0, Infinity}];
Flatten[Table[CoefficientList[FullSimplify[Numerator[p[x, n]]/x], x]/2^(1 + Floor[n/2]), {n, 1, 10}]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|