A027628 Expansion of Molien series for 5-dimensional group G_3 acting on Jacobi polynomials of ternary self-dual codes.

1, 96, 944, 4057, 11811, 27446, 55066, 99639, 166997, 263836, 397716, 577061, 811159, 1110162, 1485086, 1947811, 2511081, 3188504, 3994552, 4944561, 6054731, 7342126, 8824674, 10521167, 12451261, 14635476, 17095196, 19852669, 22931007, 26354186, 30147046

Offset

0,2

References

Michio Ozeki (ozeki(AT)sci.kj.yamagata-u.ac.jp), paper in preparation.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (1 + 91*x + 474*x^2 + 287*x^3 + 11*x^4) / (1-x)^5.

From Colin Barker, Jan 03 2017: (Start)

a(n) = (2 + 13*n + 33*n^2 + 72*n^3 + 72*n^4) / 2.

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)

E.g.f.: (2 +190*x +753*x^2 +504*x^3 +72*x^4)*exp(x)/2. - G. C. Greubel, Feb 01 2020

Maple

seq( (2 +13*n +33*n^2 +72*n^3 +72*n^4)/2, n=0..40); # G. C. Greubel, Feb 01 2020

Mathematica

CoefficientList[Series[(1 +91x +474x^2 +287x^3 +11x^4)/(1-x)^5, {x, 0, 30}], x] (* Michael De Vlieger, Jan 03 2017 *)

Prog

(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
(Magma) [(2 +13*n +33*n^2 +72*n^3 +72*n^4)/2: n in [0..40]]; // G. C. Greubel, Feb 01 2020
(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

Crossrefs

Cf. A027629, A027630.

Sequence in context: A203979 A296960 A202583 * A182684 A232918 A187165

Adjacent sequences: A027625 A027626 A027627 * A027629 A027630 A027631

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved