A258702 Coefficients in Molien series for 5-dimensional faithful representation of Horrocks-Mumford group G_{HM}.

1, 0, 1, 2, 6, 6, 21, 27, 48, 73, 112, 149, 224, 289, 390, 507, 656, 812, 1037, 1259, 1545, 1866, 2245, 2648, 3158, 3679, 4300, 4983, 5757, 6579, 7554, 8562, 9713, 10960, 12339, 13798, 15463, 17190, 19111, 21170, 23409, 25767, 28392, 31116, 34092, 37255, 40654, 44219, 48119, 52162, 56523

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Yang-Hui He, John McKay, Sporadic and Exceptional, arXiv:1505.06742 [math.AG], 2015.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,-1,2,-3,3,-2,1,1,-1,1,-2,1).

Formula

The Molien series is (1 - 2*z^5 + 2*z^10 - z^15 + 4*z^20 - 4*z^25 + 12*z^30 - 9*z^35 + 12*z^40 - 4*z^45 + 4*z^50 - z^55 + 2*z^60 - 2*z^65 + z^70)/((1 - z^30)*(1 - z^20)*(1 - z^15)*(1 - z^5)^2); the terms for n != 0 mod 5 are omitted in this sequence.

G.f.: -(x^14 -2*x^13 +2*x^12 -x^11 +4*x^10 -4*x^9 +12*x^8 -9*x^7 +12*x^6 -4*x^5 +4*x^4 -x^3 +2*x^2 -2*x +1) / ((x -1)^5*(x +1)^2*(x^2 -x +1)*(x^2 +1)*(x^2 +x +1)^2). - Colin Barker, Oct 05 2015

Mathematica

CoefficientList[Series[(x^14 - 2 x^13 + 2 x^12 - x^11 + 4 x^10 - 4 x^9 + 12 x^8 - 9 x^7 + 12 x^6 - 4 x^5 + 4 x^4 - x^3 + 2 x^2 - 2 x + 1)/((1 - x)^5 (x + 1)^2 (x^2 - x + 1) (x^2 + 1) (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 06 2015 *)

Prog

(PARI) Vec(-(x^14 -2*x^13 +2*x^12 -x^11 +4*x^10 -4*x^9 +12*x^8 -9*x^7 +12*x^6 -4*x^5 +4*x^4 -x^3 +2*x^2 -2*x +1) / ((x -1)^5*(x +1)^2*(x^2 -x +1)*(x^2 +1)*(x^2 +x +1)^2) + O(x^100)) \\ Colin Barker, Oct 05 2015

Crossrefs

Sequence in context: A081518 A367767 A368001 * A320916 A119551 A100634

Adjacent sequences: A258699 A258700 A258701 * A258703 A258704 A258705

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 08 2015, based on an email from Yang-Hui He.

Status

approved