login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
Sequence in context: A098315 A006704 A324960 * A327671 A036563 A025264
KEYWORD
sign,tabl,uned
AUTHOR
Roger L. Bagula, Apr 03 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)