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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

Table of n, a(n) for n=1..50.

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

Adjacent sequences:  A174983 A174984 A174985 * A174987 A174988 A174989

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 03 2010

STATUS

approved

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Last modified June 15 02:56 EDT 2021. Contains 345042 sequences. (Running on oeis4.)