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%I #11 Oct 25 2014 13:46:37
%S 1,0,1,1,4,5,14,20,52,90,201,371,792,1485,2977,5557,10620,19354,35467,
%T 62833,110908,190860,325794,545070,903160,1471723,2374077,3775806,
%U 5945620,9247524,14246994,21711107,32790785,49043622,72740759,106941223
%N Coefficients in Molien series for a 25-dimensional representation of SO(3) wreath Z_2.
%H D. R. J. Chillingworth, R. Lauterbach and S. S. Turzi, <a href="http://arxiv.org/abs/1407.6738">Molien series and low-degree invariants for a natural action of SO(3) wreath Z_2</a>, arXiv 1407.6738, 2014.
%F Chillingworth et al. (2014) (see Eqs. 104-111 and Appendix A) give an explicit g.f.
%p Q0 := (1-t^2) *(1-t^3) *(1-t^4)^3 *(1-t^5) *(1-t^6)^2 *(1-t^7)^2
%p *(1-t^8)^2 *(1-t^9)^2 *(1-t^10)^2 *(1-t^11) *(1-t^12) *(1-t^13) ;
%p P1 := 1 -t^4 +3*t^5 +3*t^6 +4*t^7 +10*t^8 +12*t^9 +17*t^10 +25*t^11
%p +30*t^12 +36*t^13 +41*t^14 +41*t^15 +40*t^16 +36*t^17 +16*t^18 -9*t^19
%p -32*t^20 -74*t^21 -122*t^22 -168*t^23 -223*t^24 -266*t^25 -298*t^26 -
%p 324*t^27 -312*t^28 -274*t^29 -216*t^30 -108*t^31 +30*t^32
%p +183*t^33 +364*t^34 +546*t^35 +717*t^36 +871*t^37 +961*t^38 +999*t^39 +979*t^40
%p +859*t^41 +670*t^42 +413*t^43 +83*t^44 -268*t^45 -639*t^46 -1002*t^47 -
%p 1299*t^48 -1536*t^49 -1683*t^50 -1695*t^51 -1601*t^52 -1398*t^53 -1072*t^54
%p -680*t^55 -238*t^56 +238*t^57 +680*t^58 +1072*t^59 +1398*t^60 +1601*t^61 +1695*t^62
%p +1683*t^63 +1536*t^64 +1299*t^65 +1002*t^66 +639*t^67 +268*t^68 -83*t^69
%p -413*t^70 -670*t^71 -859*t^72 -979*t^73 -999*t^74 -961*t^75 -871*t^76
%p -717*t^77 -546*t^78 -364*t^79 -183*t^80 -30*t^81 +108*t^82 +216*t^83 +274*t^84
%p +312*t^85 +324*t^86 +298*t^87 +266*t^88 +223*t^89 +168*t^90 +122*t^91 +74*t^92
%p +32*t^93 +9*t^94 -16*t^95 -36*t^96 -40*t^97 -41*t^98 -41*t^99 -36*t^100
%p -30*t^101 -25*t^102 -17*t^103 -12*t^104 -10*t^105 -4*t^106 -3*t^107
%p -3*t^108 +t^109 -t^113 ;
%p Q1 := Q0 ;
%p P0 := 1 +t^4 +3*t^5 +11*t^6 +16*t^7 +42*t^8 +80*t^9 +185*t^10 +357*t^11
%p +752*t^12 +1412*t^13 +2723*t^14 +4937*t^15 +8888*t^16 +15342*t^17
%p +26146*t^18 +43083*t^19 +69884*t^20 +110398*t^21 +171406*t^22 +260288*t^23
%p +388723*t^24 +569210*t^25 +820356*t^26 +1161726*t^27 +1620330*t^28
%p +2224150*t^29 +3009500*t^30
%p +4012238*t^31 +5276926*t^32 +6845013*t^33 +8764870*t^34 +11078260*t^35
%p +13830477*t^36 +17054459*t^37 +20782913*t^38 +25029615*t^39
%p +29802829*t^40 +35086893*t^41 +40855850*t^42 +47055721*t^43 +53620919*t^44
%p +60456820*t^45 +67458001*t^46 +74494882*t^47 +81431353*t^48 +88115150*t^49
%p +94396925*t^50 +100121953*t^51 +105148447*t^52 +109343460*t^53 +112595858*t^54
%p +114815204*t^55 +115941062*t^56 +115941062*t^57 +114815204*t^58 +112595858*t^59
%p +109343460*t^60 +105148447*t^61 +100121953*t^62 +94396925*t^63 +88115150*t^64
%p +81431353*t^65 +74494882*t^66 +67458001*t^67 +60456820*t^68 +53620919*t^69
%p +47055721*t^70 +40855850*t^71 +35086893*t^72 +29802829*t^73 +25029615*t^74
%p +20782913*t^75 +17054459*t^76 +13830477*t^77 +11078260*t^78 +8764870*t^79
%p +6845013*t^80 +5276926*t^81 +4012238*t^82 +3009500*t^83 +2224150*t^84
%p +1620330*t^85 +1161726*t^86 +820356*t^87 +569210*t^88 +388723*t^89 +260288*t^90
%p +171406*t^91 +110398*t^92 +69884*t^93 +43083*t^94 +26146*t^95 +15342*t^96
%p +8888*t^97 +4937*t^98 +2723*t^99 +1412*t^100 +752*t^101 +357*t^102 +185*t^103
%p +80*t^104 +42*t^105 +16*t^106 +11*t^107 +3*t^108 +t^109 +t^113 ;
%p gfPGamma12 := P1/Q1 ;
%p gfPGamma02 := P0/Q0 ;
%p series((gfPGamma12+gfPGamma02)/2,t=0,100) ;
%p gfun[seriestolist](%) ; # _R. J. Mathar_, Oct 25 2014
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Sep 15 2014
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