%I A027640
%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,
%T A027640 0,10,0,11,0,12,0,14,1,17,0,16,1,21,1,22,1,24,2,27,3,31,
%U A027640 2,31,4,37,4,39,5,42,6,46,8,52,7,52,10,60,11,63,12,67,14
%N A027640 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). [From 
               Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009]
%D A027640 J. Igusa, On Siegel modular forms of genus 2 (II), Amer. J. Math., 86 
               (1964), 392-412, esp. p. 402.
%D A027640 B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 
               57-85.
%p A027640 (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}] [From Kilian Kilger (kilian(AT)nihilnovi.de), 
               Sep 24 2009]
%Y A027640 C.f. A165685 for the corresponding dimension of the space of cusp forms. 
               [From Kilian Kilger (kilian(AT)nihilnovi.de), Sep 24 2009]
%Y A027640 Sequence in context: A128144 A128145 A128143 this_sequence A127460 A154109 
               A011374
%Y A027640 Adjacent sequences: A027637 A027638 A027639 this_sequence A027641 A027642 
               A027643
%K A027640 nonn
%O A027640 0,11
%A A027640 N. J. A. Sloane (njas(AT)research.att.com).