A027630 Molien series for Gamma_3(2).

1, 15, 135, 870, 3992, 14142, 41400, 104870, 237288, 490654, 942888, 1705510, 2932344, 4829246, 7664856, 11782374, 17612360, 25686558, 36652744, 51290598, 70528600, 95461950, 127371512, 167743782, 218291880, 280977566, 358034280, 451991206, 565698360

Offset

0,2

Links

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

B. Runge, On Siegel modular forms II, Nagoya Math. J., 138 (1995), 179-197.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (1 - x^4)*(1 + 7*x + 43*x^2 + 154*x^3 + 43*x^4 + 7*x^5 + x^6) / (1-x)^8.

From Colin Barker, Jan 03 2017: (Start)

a(n) = 2*(3060 -6138*n +5933*n^2 -3120*n^3 +1100*n^4 -192*n^5 +32*n^6)/45 for n>2.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9. (End)

E.g.f.: (-12150 -1350*x -45*x^2 + (12240 -9540*x +9540*x^2 +6240*x^3 + 5040*x^4 +1152*x^5 +128*x^6)*exp(x))/90. - G. C. Greubel, Feb 01 2020

Maple

1, seq( `if`(n<3, 15*(2*n-1)^2, 2*(3060 -6138*n +5933*n^2 -3120*n^3 +1100*n^4 -192*n^5 +32*n^6)/45), n=1..30); # G. C. Greubel, Feb 01 2020

Mathematica

Table[If[n==0, 1, If[n<3, 15*(2*n-1)^2, 2*(3060 -6138*n +5933*n^2 -3120*n^3 + 1100*n^4 -192*n^5 +32*n^6)/45]], {n, 0, 30}] (* G. C. Greubel, Feb 01 2020 *)

Prog

(PARI) Vec((1+x)*(1+x^2)*(1+7*x+43*x^2+154*x^3+43*x^4+7*x^5+x^6) / (1-x)^7 + O(x^30)) \\ Colin Barker, Jan 03 2017
(Magma) [1, 15, 135] cat [2*(3060 -6138*n +5933*n^2 -3120*n^3 +1100*n^4 -192*n^5 +32*n^6)/45: n in [3..30]]; // G. C. Greubel, Feb 01 2020
(Sage) [1, 15, 135]+[2*(3060 -6138*n +5933*n^2 -3120*n^3 +1100*n^4 -192*n^5 +32*n^6)/45 for n in (3..30)] # G. C. Greubel, Feb 01 2020
(GAP) Concatenation([1, 15, 135], List([3..30], n-> 2*(3060 -6138*n +5933*n^2 -3120*n^3 +1100*n^4 -192*n^5 +32*n^6)/45 )); # G. C. Greubel, Feb 01 2020

Crossrefs

Cf. A027628, A027629.

Sequence in context: A201138 A230659 A228583 * A027629 A023013 A036217

Adjacent sequences: A027627 A027628 A027629 * A027631 A027632 A027633

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved