A246983 Coefficients in Molien series for a 25-dimensional representation of SO(3) X SO(3).

1, 0, 1, 1, 5, 5, 19, 27, 76, 136, 330, 626, 1391, 2676, 5497, 10425, 20201, 37182, 68713, 122489, 217275, 375356, 642745, 1077968, 1789674, 2920958, 4717966, 7511437, 11838092, 18425307, 28403043, 43304420, 65429758, 97892886

Offset

0,5

Links

Table of n, a(n) for n=0..33.

D. R. J. Chillingworth, R. Lauterbach and S. S. Turzi, Molien series and low-degree invariants for a natural action of SO(3) wreath Z_2, arXiv 1407.6738, 2014.

Formula

Theorem 2 (see also Appendix A) gives an explicit g.f.

Maple

Q0 := (1-t^2) *(1-t^3) *(1-t^4)^3 *(1-t^5) *(1-t^6)^2 *(1-t^7)^2
*(1-t^8)^2 *(1-t^9)^2 *(1-t^10)^2 *(1-t^11) *(1-t^12) *(1-t^13) ;
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
+752*t^12 +1412*t^13 +2723*t^14 +4937*t^15 +8888*t^16 +15342*t^17
+26146*t^18 +43083*t^19 +69884*t^20 +110398*t^21 +171406*t^22 +260288*t^23
+388723*t^24 +569210*t^25 +820356*t^26 +1161726*t^27 +1620330*t^28
+2224150*t^29 +3009500*t^30
+4012238*t^31 +5276926*t^32 +6845013*t^33 +8764870*t^34 +11078260*t^35
+13830477*t^36 +17054459*t^37 +20782913*t^38 +25029615*t^39
+29802829*t^40 +35086893*t^41 +40855850*t^42 +47055721*t^43 +53620919*t^44
+60456820*t^45 +67458001*t^46 +74494882*t^47 +81431353*t^48 +88115150*t^49
+94396925*t^50 +100121953*t^51 +105148447*t^52 +109343460*t^53 +112595858*t^54
+114815204*t^55 +115941062*t^56 +115941062*t^57 +114815204*t^58 +112595858*t^59
+109343460*t^60 +105148447*t^61 +100121953*t^62 +94396925*t^63 +88115150*t^64
+81431353*t^65 +74494882*t^66 +67458001*t^67 +60456820*t^68 +53620919*t^69
+47055721*t^70 +40855850*t^71 +35086893*t^72 +29802829*t^73 +25029615*t^74
+20782913*t^75 +17054459*t^76 +13830477*t^77 +11078260*t^78 +8764870*t^79
+6845013*t^80 +5276926*t^81 +4012238*t^82 +3009500*t^83 +2224150*t^84
+1620330*t^85 +1161726*t^86 +820356*t^87 +569210*t^88 +388723*t^89 +260288*t^90
+171406*t^91 +110398*t^92 +69884*t^93 +43083*t^94 +26146*t^95 +15342*t^96
+8888*t^97 +4937*t^98 +2723*t^99 +1412*t^100 +752*t^101 +357*t^102 +185*t^103
+80*t^104 +42*t^105 +16*t^106 +11*t^107 +3*t^108 +t^109 +t^113 ;
P0/Q0 ;
series(%, t=0, 100) ;
gfun[seriestolist](%) ; # R. J. Mathar, Oct 25 2014

Crossrefs

Sequence in context: A147141 A146146 A145937 * A305514 A039914 A274910

Adjacent sequences: A246980 A246981 A246982 * A246984 A246985 A246986

Keyword

nonn

Author

N. J. A. Sloane, Sep 15 2014

Status

approved