OFFSET
0,5
COMMENTS
Difference of the number of partitions of n+5 into 5 parts and the number of partitions of n+5 into 6 parts. - Wesley Ivan Hurt, Apr 16 2019
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
P. A. MacMahon, Perpetual reciprocants, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).
FORMULA
G.f.: (1 - x - x^6) / ((1 - x)^6*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 17 2019
MATHEMATICA
With[{nn=6}, CoefficientList[Series[(1-x-x^nn)/Times@@(1-x^Range[nn]), {x, 0, 60}], x]] (* Harvey P. Dale, May 15 2016 *)
PROG
(PARI) Vec((1 - x - x^6) / ((1 - x)^6*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Apr 17 2019
(Magma) m:=6; R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x-x^m)/( (&*[1-x^j: j in [1..m]]) ) )); // G. C. Greubel, Apr 17 2019
(Sage) m=6; ((1-x-x^m)/( product(1-x^j for j in (1..m)) )).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Apr 17 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Mar 17 2001
STATUS
approved