%I #21 Sep 08 2022 08:44:49
%S 1,96,944,4057,11811,27446,55066,99639,166997,263836,397716,577061,
%T 811159,1110162,1485086,1947811,2511081,3188504,3994552,4944561,
%U 6054731,7342126,8824674,10521167,12451261,14635476,17095196,19852669,22931007,26354186,30147046
%N Expansion of Molien series for 5-dimensional group G_3 acting on Jacobi polynomials of ternary self-dual codes.
%D Michio Ozeki (ozeki(AT)sci.kj.yamagata-u.ac.jp), paper in preparation.
%H Colin Barker, <a href="/A027628/b027628.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: (1 + 91*x + 474*x^2 + 287*x^3 + 11*x^4) / (1-x)^5.
%F From _Colin Barker_, Jan 03 2017: (Start)
%F a(n) = (2 + 13*n + 33*n^2 + 72*n^3 + 72*n^4) / 2.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End)
%F E.g.f.: (2 +190*x +753*x^2 +504*x^3 +72*x^4)*exp(x)/2. - _G. C. Greubel_, Feb 01 2020
%p seq( (2 +13*n +33*n^2 +72*n^3 +72*n^4)/2, n=0..40); # _G. C. Greubel_, Feb 01 2020
%t CoefficientList[Series[(1 +91x +474x^2 +287x^3 +11x^4)/(1-x)^5, {x, 0, 30}], x] (* _Michael De Vlieger_, Jan 03 2017 *)
%o (PARI) Vec((1+91*x+474*x^2+287*x^3+11*x^4)/(1-x)^5 + O(x^40)) \\ _Colin Barker_, Jan 03 2017
%o (Magma) [(2 +13*n +33*n^2 +72*n^3 +72*n^4)/2: n in [0..40]]; // _G. C. Greubel_, Feb 01 2020
%o (Sage) [(2 +13*n +33*n^2 +72*n^3 +72*n^4)/2 for n in (0..40)] # _G. C. Greubel_, Feb 01 2020
%Y Cf. A027629, A027630.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_