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 A099750 Molien series for complete weight enumerators of doubly-even Euclidean self-dual codes over the Galois ring GR(4,2). 1
 1, 3, 22, 346, 5100, 53504, 411041, 2471091, 12244665, 51924492, 193733585, 649448814, 1988025385, 5628317525, 14888914321, 37110706136, 87756490312, 198017040530, 428428858514, 892492579595, 1796484842799, 3504861873102, 6645228329464, 12273264853180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 S.-P. Eu, T.-S. Fu, Y.-J. Pan and C.-T. Ting, Baxter Permutations, Maj-balances, and Positive Braids, Electronic Journal of Combinatorics, 19(3) (2012), #P26. - From N. J. A. Sloane, Dec 25 2012 G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. FORMULA 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(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. MAPLE 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): u1:= f(t) + t^39*f(t^(-1)): u2:=  (1-t)^3*(1-t^2)^5*(1-t^3)^5*(1-t^5)^3: S:= series(u1/u2, t, 51): seq(coeff(S, t, j), j=0..50); # Robert Israel, May 02 2016 CROSSREFS Sequence in context: A046947 A002485 A193193 * A219268 A259919 A275366 Adjacent sequences:  A099747 A099748 A099749 * A099751 A099752 A099753 KEYWORD nonn AUTHOR G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10 2004 STATUS approved

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Last modified April 9 17:09 EDT 2020. Contains 333361 sequences. (Running on oeis4.)