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A058923 a(n) = binomial(n,0) - binomial(n,2) + binomial(n,4). 1
1, 1, 0, -2, -4, -4, 1, 15, 43, 91, 166, 276, 430, 638, 911, 1261, 1701, 2245, 2908, 3706, 4656, 5776, 7085, 8603, 10351, 12351, 14626, 17200, 20098, 23346, 26971, 31001, 35465, 40393, 45816, 51766, 58276, 65380, 73113, 81511, 90611, 100451, 111070, 122508 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

From R. J. Mathar, Mar 17 2009: (Start)

a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5).

G.f.: -(1-4*x-2*x^3+x^4+5*x^2)/(x-1)^5. (End)

MATHEMATICA

CoefficientList[Series[-((z - 1)*z*((z - 1)*z + 4) + 1)/(z - 1)^5, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 16 2011 *)

Table[Binomial[n, 0]-Binomial[n, 2]+Binomial[n, 4], {n, 0, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 0, -2, -4}, 50] (* Harvey P. Dale, Mar 02 2015 *)

PROG

(PARI) { for (n = 0, 200, write("b058923.txt", n, " ", 1 - binomial(n, 2) + binomial(n, 4)); ) } \\ Harry J. Smith, Jun 24 2009

(PARI) Vec(-(1-4*x-2*x^3+x^4+5*x^2)/(x-1)^5 + O(x^60)) \\ Michel Marcus, Jan 03 2016

CROSSREFS

Cf. A000127.

Sequence in context: A307059 A328412 A079536 * A107500 A108620 A070512

Adjacent sequences:  A058920 A058921 A058922 * A058924 A058925 A058926

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Jan 12 2001

STATUS

approved

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Last modified May 15 17:50 EDT 2021. Contains 343920 sequences. (Running on oeis4.)