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%I #20 Jan 27 2021 15:02:07
%S 1,2,13,87,472,2099,7651,23632,64007,155869,347888,722562,1412787,
%T 2623960,4663042,7975064,13188959,21174366,33109962,50565794,75601497,
%U 110881127,159807508,226678408,316865230,437017617,595296931,801638887,1068049576,1408938228
%N Molien series for genus 2 complete weight enumerators of self-dual codes over GF(3) containing the all-ones vector.
%C The invariant ring for a 9-dimensional group Z_4 X 3^{1+4}_{+}.SP_4(3) of order 50388480.
%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1,-6,7,-3,4,-5,7,-5,-4,0,4,5,-7,5,-4,3,-7,6,-1,2,-3,1).
%p # (Maple code for Molien series:)
%p f := 1+8*t^2+60*t^3+292*t^4+1090*t^5+3127*t^6+7116*t^7 +13411*t^8 + 21536*t^9+29963*t^10+36631*t^11+39638*t^12 +37973*t^13+32135*t^14+ 23906*t^15+15462*t^16+8507*t^17 +3858*t^18+1369*t^19+342*t^20+52*t^21+3*t^22;
%p u1 := subs(t=t^12,f); u2 := (1-t^12)^2*(1-t^24)^2*(1-t^36)^3*(1-t^60)^2; MS := u1/u2;
%p seq(coeff(series(MS, t, 12*n+3), t, 12*n), n=0..30);
%t CoefficientList[Series[(1+8*x^2+60*x^3+292*x^4+1090*x^5+3127*x^6+7116*x^7 +13411*x^8 + 21536*x^9+29963*x^10+36631*x^11+39638*x^12 +37973*x^13+32135*x^14+ 23906*x^15+15462*x^16+8507*x^17 +3858*x^18+1369*x^19+342*x^20+52*x^21+3*x^22) / (-(x+1)^2*(x^4+x^3+x^2+x+1)^2*(x^2+x+1)^3*(x-1)^9), {x, 0, 28}], x] (* _Georg Fischer_, Jan 25 2021 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 30 2004
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