OFFSET
0,11
COMMENTS
a(k) for k>0 is the dimension of the space of Siegel modular forms of genus 2 and weight k (for the full modular group Gamma_2). - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009
REFERENCES
B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
J. Igusa, On Siegel modular forms of genus 2 (II), Amer. J. Math., 86 (1964), 392-412, esp. p. 402.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,1,0,0,1,-1,-1,-1,0,0,1,1,1,0,0,0,-1).
FORMULA
G.f.: (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)).
MATHEMATICA
Table[SeriesCoefficient[Series[(1+t^(35))/((1-t^4) (1-t^6)(1-t^(10)) (1-t^(12))), {t, 0, 100}], i], {i, 0, 100}] (* Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009 *)
PROG
(PARI) Vec((1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) + O(x^100)) \\ Colin Barker, Jul 27 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) )); // G. C. Greubel, Aug 04 2022
(Sage)
def A027640_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) ).list()
A027640_list(100) # G. C. Greubel, Aug 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved