This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027640 #31 Jul 07 2025 03:30:59
%S A027640 1,0,0,0,1,0,1,0,1,0,2,0,3,0,2,0,4,0,4,0,5,0,6,0,8,0,7,0,10,0,11,0,12,
%T A027640 0,14,1,17,0,16,1,21,1,22,1,24,2,27,3,31,2,31,4,37,4,39,5,42,6,46,8,
%U A027640 52,7,52,10,60,11,63,12,67,14,73,17,80,16,81,21,91,22,95
%N A027640 Poincaré series [or Poincare series] for ring of modular forms of genus 2.
%C A027640 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
%H A027640 Colin Barker, <a href="/A027640/b027640.txt">Table of n, a(n) for n = 0..1000</a>
%H A027640 J. Igusa, <a href="http://www.jstor.org/stable/2373172">On Siegel modular forms of genus 2 (II)</a>, Amer. J. Math., 86 (1964), 392-412, esp. p. 402.
%H A027640 Bernhard Runge, <a href="https://eudml.org/doc/153497">On Siegel modular forms. Part I</a>, J. Reine Angew. Math., 436 (1993), 57-85.
%H A027640 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A027640 G.f.: (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)).
%t A027640 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 *)
%o A027640 (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
%o A027640 (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
%o A027640 (Sage)
%o A027640 def A027640_list(prec):
%o A027640 P.<x> = PowerSeriesRing(ZZ, prec)
%o A027640 return P( (1+x^35)/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)) ).list()
%o A027640 A027640_list(100) # _G. C. Greubel_, Aug 04 2022
%Y A027640 Cf. A165685 for the corresponding dimension of the space of cusp forms. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009
%K A027640 nonn,easy
%O A027640 0,11
%A A027640 _N. J. A. Sloane_