A099750 - OEIS

%I #18 May 03 2016 10:33:17

%S 1,3,22,346,5100,53504,411041,2471091,12244665,51924492,193733585,

%T 649448814,1988025385,5628317525,14888914321,37110706136,87756490312,

%U 198017040530,428428858514,892492579595,1796484842799,3504861873102,6645228329464,12273264853180

%N Molien series for complete weight enumerators of doubly-even Euclidean self-dual codes over the Galois ring GR(4,2).

%H Robert Israel, <a href="/A099750/b099750.txt">Table of n, a(n) for n = 0..10000</a>

%H S.-P. Eu, T.-S. Fu, Y.-J. Pan and C.-T. Ting, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p26/0">Baxter Permutations, Maj-balances, and Positive Braids</a>, Electronic Journal of Combinatorics, 19(3) (2012), #P26. - From _N. J. A. Sloane_, Dec 25 2012

%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>

%F G.f.: u1/u2 where u1 := f(t^4) + t^156*f(t^-4), u2 := (1-t^4)^3*(1-t^8)^5*(1-t^12)^5*(1-t^20)^3 and

%F f(t) = 1 + 11*t^2 + 283*t^3 + 4055*t^4 + 37722*t^5 + 243578*t^6 + 1179852*t^7 + 4535052*t^8 + 14380814*t^9 + 38708195*t^10 + 90379766*t^11 + 186147868*t^12 + 342605290*t^13 + 569177435*t^14 + 860160090*t^15+ 1189401593*t^16+ 1511365669*t^17+ 1770220838*t^18+ 1914917488*t^19.

%p f:= unapply(1 + 11*t^2 + 283*t^3 + 4055*t^4 + 37722*t^5 + 243578*t^6 + 1179852*t^7 + 4535052*t^8 + 14380814*t^9 + 38708195*t^10 + 90379766*t^11 + 186147868*t^12 + 342605290*t^13 + 569177435*t^14 + 860160090*t^15+ 1189401593*t^16+ 1511365669*t^17+ 1770220838*t^18+ 1914917488*t^19, t):

%p u1:= f(t) + t^39*f(t^(-1)):

%p u2:=  (1-t)^3*(1-t^2)^5*(1-t^3)^5*(1-t^5)^3:

%p S:= series(u1/u2, t, 51):

%p seq(coeff(S,t,j),j=0..50); # _Robert Israel_, May 02 2016

%K nonn

%O 0,2

%A G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10 2004