%I #13 Oct 31 2021 15:44:24

%S 1,13,673,8485,54806,239653,810554,2286970,5645962,12569202,25774647,

%T 49439178,89715139,155363247,258516275,415556399,648154544,984466839,

%U 1460477524,2121535332,3024090172,4237589492,5846620281,7953274324,10679706157,14170967905

%N Molien series for complete weight enumerators of Type II self-dual codes over Z/8Z containing the all-ones vector.

%H G. C. Greubel, <a href="/A092547/b092547.txt">Table of n, a(n) for n = 0..1000</a>

%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/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2,-4,4,9,-5,-6,-5,9,4,-4,-2,-1,3,-1).

%F G.f.: u1/u2 where u1 := subs(x=x^16, f); u2 := (1-x^16 )^3*(1-x^32 )^2*(1-x^48 )^3; and f := 1 + 10*x + 635*x^2 + 6481*x^3 + 30054*x^4 + 85114 *x^5 + 166002 *x^6 + 235709 *x^7 + 254210 *x^8 + 205865 *x^9 + 123812 *x^10 + 53334 *x^11 + 15059 *x^12 + 2247 *x^13 + 115 *x^14.

%F G.f.: (1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 ). - _G. C. Greubel_, Feb 02 2020

%p f(x):= (1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 );

%p seq(coeff(series( f(x), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Feb 02 2020

%t CoefficientList[Series[(1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 ), {x,0,30}], x] (* _G. C. Greubel_, Feb 02 2020 *)

%t LinearRecurrence[{3,-1,-2,-4,4,9,-5,-6,-5,9,4,-4,-2,-1,3,-1},{1,13,673,8485,54806,239653,810554,2286970,5645962,12569202,25774647,49439178,89715139,155363247,258516275,415556399},30] (* _Harvey P. Dale_, Oct 31 2021 *)

%Y Cf. A092544, A092545, A092546.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 09 2004