A091778 - OEIS

A091778

G.f.: Product((1+x^i)/(1-x^i),i=1..n-1)/(1-x^n), with n = 7.

1, 2, 4, 8, 14, 24, 40, 63, 96, 144, 210, 300, 422, 582, 791, 1062, 1406, 1840, 2384, 3056, 3882, 4891, 6110, 7576, 9330, 11412, 13872, 16766, 20149, 24088, 28658, 33932, 39998, 46952, 54890, 63925, 74178, 85772, 98848, 113558, 130056, 148516, 169125, 192072

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OFFSET

0,2

COMMENTS

Poincaré series [or Poincare series] (or Molien series) for H^*(O_7(q); F_2).

REFERENCES

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 233.

LINKS

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,7,-9,10,-9,9,-10,9,-7,6,-7,6,-3,3,-3,1).

FORMULA

G.f.: -(x^2+1)*(x^4-x^3+x^2-x+1)*(x^4-x^2+1)*(x^4+1) / ((x-1)^7*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)). [Colin Barker, Jan 31 2013]

MATHEMATICA

CoefficientList[Series[(Product[(1+x^i)/(1-x^i), {i, 6}])/(1-x^7), {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 3, -6, 7, -6, 7, -9, 10, -9, 9, -10, 9, -7, 6, -7, 6, -3, 3, -3, 1}, {1, 2, 4, 8, 14, 24, 40, 63, 96, 144, 210, 300, 422, 582, 791, 1062, 1406, 1840, 2384, 3056, 3882}, 50] (* Harvey P. Dale, Mar 10 2019 *)

CROSSREFS

Sequence in context: A243815 A060046 A053801 * A053802 A091779 A365666

Adjacent sequences: A091775 A091776 A091777 * A091779 A091780 A091781

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 18 2004

STATUS

approved