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A092545 Molien series for complete weight enumerators of self-dual codes over Z/8Z containing the all-ones vector. 4
1, 3, 44, 361, 2010, 7952, 25401, 68662, 164459, 357241, 718934, 1357271, 2431460, 4164014, 6864051, 10942908, 16946805, 25576479, 37731200, 54532437, 77381198, 107985724, 148434413, 201227282, 269366687, 356392309, 466492202, 604540771 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for Molien series

FORMULA

G.f.: u1/u2 where u1 := subs(x=x^8, f); f := 1 + 35*x^2 + 237*x^3 + 943*x^4 + 2250*x^5 + 4089*x^6 + 5659*x^7 + 6323*x^8 + 5680*x^9 + 4057*x^10 + 2311*x^11 + 909*x^12 + 246*x^13 + 27*x^14 + x^15; u2 := (1-x^8)^3*(1-x^16 )^3*(1-x^32 )^2.

MAPLE

f(x):= (1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2);

seq(coeff(series( f(x), x, n+1), x, n), n = 0..30); # G. C. Greubel, Feb 02 2020

MATHEMATICA

CoefficientList[Series[(1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2), {x, 0, 30}], x] (* G. C. Greubel, Feb 02 2020 *)

CROSSREFS

Cf. A092544, A092545, A092546, A092547.

Sequence in context: A055539 A046946 A327360 * A011916 A337249 A259785

Adjacent sequences:  A092542 A092543 A092544 * A092546 A092547 A092548

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 09 2004

STATUS

approved

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Last modified September 29 10:06 EDT 2020. Contains 337428 sequences. (Running on oeis4.)