A091769 Poincaré series [or Poincare series] (or Molien series) for a certain six-fold wreath product P_6.
1, 0, 1, 1, 2, 2, 5, 4, 9, 10, 16, 19, 32, 35, 55, 67, 95, 117, 166, 199, 276, 339, 449, 555, 731, 889, 1154, 1413, 1794, 2193, 2764, 3347, 4181, 5058, 6233, 7519, 9208, 11027, 13411, 16015, 19307, 22970, 27538, 32582, 38851, 45805, 54265, 63747, 75170, 87896, 103179
Offset: 0
Keywords
References
- A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004, p. 203.
Links
- Ray Chandler, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-2,0,3,-5,7,-7,4,-2,2,-1,-1,4,-6,6,-6,5,-3,-1,6,-6, 2,1,-4,5,-3,4,-5,2,-1,0,4,-6,9,-12,8,-2,-1,4,-6,6,-6,6,-6, 4,-1,-2,8,-12,9,-6,4,0,-1,2,-5,4,-3,5,-4,1,2,-6,6,-1,-3,5, -6,6,-6,4,-1,-1,2,-2,4,-7,7,-5,3,0,-2,2,-3,3,-1).
Programs
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Mathematica
CoefficientList[Series[(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) * (1-2*x+x^2+ x^5-x^6+x^10-x^11+2*x^12-2*x^13+x^14-x^15+x^16+x^17-x^18+x^19-x^21+2*x^22 - 2*x^23+3*x^24-2*x^25+2*x^26-x^27+x^29-x^30 +x^31+x^32-x^33+x^34-2*x^35+2*x^36 - x^37+x^38-x^42+x^43+x^46-2*x^47+x^48) / ((1-x)^3*(1-x^3)*(1-x^4)*(1-x^6)*(1- x^8)*(1-x^9)*(1-x^12)*(1-x^10)*(1-x^15)*(1-x^18)), {x,0,60}], x] (* G. C. Greubel, Jan 31 2020 *)
Formula
G.f.: ( x^75 + x^70 + x^68 + x^67 + x^66 + 2*x^65 + 2*x^64 + 2*x^63 + 3*x^62 + 4*x^61 + 4*x^60 + 5*x^59 + 5*x^58 + 6*x^57 + 7*x^56 + 8*x^55 + 10*x^54 + 10*x^53 + 11*x^52 + 13*x^51 + 14*x^50 + 15*x^49 + 17*x^48 + 18*x^47 + 19*x^46 + 20*x^45 + 21*x^44 + 22*x^43 + 23*x^42 + 23*x^41 + 24*x^40 + 23*x^39 + 24*x^38 + 24*x^37 + 23*x^36 + 24*x^35 + 23*x^34 + 23*x^33 + 22*x^32 + 21*x^31 + 20*x^30 + 19*x^29 + 18*x^28 + 17*x^27 + 15*x^26 + 14*x^25 + 13*x^24 + 11*x^23 + 10*x^22 + 10*x^21 + 8*x^20 + 7*x^19 + 6*x^18 + 5*x^17 + 5*x^16 + 4*x^15 + 4*x^14 + 3*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + x^9 + x^8 + x^7 + x^5 + 1 ) / ( (1 - x^2)*(1- x^3)*(1 - x^4)*(1 - x^6)^2*( 1- x^8)*(1 - x^9)*(1 - x^12)^2 *(1 - x^10)*(1 - x^15)*(1 - x^18)).