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Coefficients in Molien series for a 25-dimensional representation of SO(3) X SO(3).
0

%I #7 Oct 25 2014 12:40:10

%S 1,0,1,1,5,5,19,27,76,136,330,626,1391,2676,5497,10425,20201,37182,

%T 68713,122489,217275,375356,642745,1077968,1789674,2920958,4717966,

%U 7511437,11838092,18425307,28403043,43304420,65429758,97892886

%N Coefficients in Molien series for a 25-dimensional representation of SO(3) X SO(3).

%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 Theorem 2 (see also Appendix A) gives 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 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 P0/Q0 ;

%p series(%,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