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A030535 Expansion of Molien series for 16-D extraspecial group 2^{1+2*4}. 4

%I

%S 1,1,51,219,2244,12815,69615,303165,1180395,4052070,12706650,36580770,

%T 98256600,247786866,592040266,1347148374,2936245389,6154632399,

%U 12456241445,24415459445,46484089740,86164059465,155843612865,275546946795,477079706295,810057618396

%N Expansion of Molien series for 16-D extraspecial group 2^{1+2*4}.

%C The first formula intersperses the terms with zeros, the second formula does not. - _Colin Barker_, Apr 01 2015

%H Colin Barker, <a href="/A030535/b030535.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%F G.f.: (x^32 -7*x^30 +63*x^28 -161*x^26 +1394*x^24 -307*x^22 +7665*x^20 +987*x^18 +13498*x^16 +987*x^14 +7665*x^12 -307*x^10 +1394*x^8 -161*x^6 +63*x^4 -7*x^2 +1)/(1 +x^2)^8/(-1 +x^2)^8/(1 +x)^8/(-1 +x)^8.

%F G.f.: (x^16 -7*x^15 +63*x^14 -161*x^13 +1394*x^12 -307*x^11 +7665*x^10 +987*x^9 +13498*x^8 +987*x^7 +7665*x^6 -307*x^5 +1394*x^4 -161*x^3 +63*x^2 -7*x +1) / ((x -1)^16*(x +1)^8). - _Colin Barker_, Apr 01 2015

%e 1+l^2+51*l^4+219*l^6+2244*l^8+12815*l^10+...

%o (PARI) Vec((x^16 -7*x^15 +63*x^14 -161*x^13 +1394*x^12 -307*x^11 +7665*x^10 +987*x^9 +13498*x^8 +987*x^7 +7665*x^6 -307*x^5 +1394*x^4 -161*x^3 +63*x^2 -7*x +1) / ((x -1)^16*(x +1)^8) + O(x^100)) \\ _Colin Barker_, Apr 01 2015

%Y Cf. A014095, A030533, A030536, A030537.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)