A027632 Molien series for group Gamma_{3,0}(2).

1, 1, 4, 6, 14, 23, 45, 72, 126, 195, 315, 472, 720, 1042, 1520, 2132, 2995, 4089, 5568, 7418, 9843, 12833, 16652, 21304, 27117, 34114, 42705, 52930, 65294, 79867, 97253, 117562, 141516, 169265, 201665, 238922, 282030, 331264, 387780, 451920, 525023, 607517

Offset

0,3

Links

Table of n, a(n) for n=0..41.

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

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, -1, 1, 4, -2, -5, 3, 4, 0, -4, -3, 5, 2, -4, -1, 1, 3, -1, -2, 1).

Formula

G.f.: N_Hecke(x)*(1 + x^2)/((1 - x^2)*(1 - x^4)^3*(1 - x^6)*(1 - x^12)*(1 - x^14)) where N_Hecke(x)= 1 - x^2 + x^4 + 2*x^8 + x^10 + 2*x^12 + x^14 + 5*x^16 + x^18 + 6*x^20 + 2*x^22 + 6*x^24 + 2*x^26 + 6*x^28 + x^30 + 5*x^32 + x^34 + 2*x^36 + x^38 + 2*x^40 + x^44 - x^46 + x^48.

Mathematica

CoefficientList[Series[-(1-x+x^2+2 x^4+x^5+2 x^6+x^7+5 x^8+x^9+6 x^10+2 x^11+6 x^12+2 x^13+6 x^14+x^15+5 x^16+x^17+2 x^18+x^19+2 x^20+x^22-x^23+x^24)/((-1+x)^7 (1+x)^3 (1-x+x^2) (1+x+x^2)^2 (1+x+x^2+x^3+x^4+x^5+x^6)), {x, 0, 30}], x] (* Peter J. C. Moses, Dec 22 2013 *)
LinearRecurrence[{2, 1, -3, -1, 1, 4, -2, -5, 3, 4, 0, -4, -3, 5, 2, -4, -1, 1, 3, -1, -2, 1}, {1, 1, 4, 6, 14, 23, 45, 72, 126, 195, 315, 472, 720, 1042, 1520, 2132, 2995, 4089, 5568, 7418, 9843, 12833, 16652, 21304, 27117}, 50] (* Harvey P. Dale, Apr 23 2022 *)

Crossrefs

Sequence in context: A210632 A097271 A126867 * A175722 A200186 A370410

Adjacent sequences: A027629 A027630 A027631 * A027633 A027634 A027635

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms and formula from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 24 2001

More terms from Peter J. C. Moses, Dec 22 2013

Status

approved