OFFSET
0,5
LINKS
Jean-François Alcover, Table of n, a(n) for n = 0..999
B. Runge, On Siegel modular forms II, Nagoya Math. J., 138 (1995), 179-197.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1, 2, -1, -1, 1, -2, 0, 0, -2, 2, 0, -1, 3, -1, 1, 2, -3, 2, 0, -3, 3, -3, 0, 3, -4, 3, 0, -3, 3, -3, 0, 2, -3, 2, 1, -1, 3, -1, 0, 2, -2, 0, 0, -2, 1, -1, -1, 2, -1, 1, 0, 0, 1, -1).
FORMULA
Reference gives explicit formula for Molien series.
Molien series is f(x)*(1 + x^2)/((1 - x^4)*(1 - x^8)*(1 - x^12)^2*(1 - x^14)*(1 - x^18)*(1 - x^20)*(1 - x^30)),
where f(x) = g(x) + x^112*g(1/x), g(x) = 1 + x^4 + x^10 + 3*x^16 - x^18 + 3*x^20 + 2*x^22 + 2*x^24 + 3*x^26 + 4*x^28 + 2*x^30 + 7*x^32 + 3*x^34 + 7*x^36 + 5*x^38 + 9*x^40 + 6*x^42 + 10*x^44 + 8*x^46 + 9*x^50 + 7*x^54 - x^2 + 12*x^52 + 10*x^48 + 7*x^56.
EXAMPLE
1 + x^4 + x^6 + 2*x^8 + 2*x^10 + 5*x^12 + 4*x^14 + 9*x^16 + 10*x^18 + 16*x^20 + ...
PROG
(Sage)
R.<x> = PowerSeriesRing(ZZ, 40);
g = 1 + x^4 + x^10 + 3*x^16 - x^18 + 3*x^20 + 2*x^22 + 2*x^24 + 3*x^26 + 4*x^28 + 2*x^30 + 7*x^32 + 3*x^34 + 7*x^36 + 5*x^38 + 9*x^40 + 6*x^42 + 10*x^44 + 8*x^46 + 9*x^50 + 7*x^54 - x^2 + 12*x^52 + 10*x^48 + 7*x^56;
f = g + x^112*g(1/x);
h = f(x)*(1 + x^2)/((1 - x^4)*(1 - x^8)*(1 - x^12)^2*(1 - x^14)*(1 - x^18)*(1 - x^20)*(1 - x^30));
[h.list()[2*i] for i in range(20)] # Andy Huchala, Mar 02 2022
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved