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A027628 Expansion of Molien series for 5-dimensional group G_3 acting on Jacobi polynomials of ternary self-dual codes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 03:19 EST 2021. Contains 349562 sequences. (Running on oeis4.)