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%I #18 Aug 05 2022 07:42:35
%S 1,0,0,0,2,0,2,0,4,0,5,0,9,0,9,0,15,0,17,1,23,1,27,3,36,3,39,6,51,7,
%T 57,11,69,13,78,19,94,21,102,29,122,33,134,42,154,48,170,60,195,66,
%U 210,81,240,90,260,106,290,118,315,138,351,150,375,174,417
%N Poincaré series [or Poincare series] for Gamma_2(1,2).
%H Takeyoshi Kogiso and Koji Tsushima, <a href="https://doi.org/10.21099/tkbjm/1496163670">On an algebra of Siegel modular forms associated with the theta group Gamma_2(1,2)</a>, Tsukuba J. Math. 22 (1998), 645-656.
%H B. Runge, <a href="https://doi.org/10.1016/0012-365X(94)00271-J">Codes and Siegel modular forms</a>, Discrete Math. 148 (1996), 175-204, p. 203, first displayed formula.
%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,-1,1,0,0,1,-1).
%p (1+x^6+x^8+x^10+x^19+x^21+x^23+x^29)/((1-x^4)^2*(1-x^6)*(1-x^12));
%t Join[{1, 0, 0, 0}, LinearRecurrence[{1, 0, 0, 1, -1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1}, {2, 0, 2, 0, 4, 0, 5, 0, 9, 0, 9, 0, 15, 0, 17, 1, 23, 1, 27, 3, 36, 3, 39}, 61]] (* _Jean-François Alcover_, Jul 31 2019 *)
%K nonn,nice,easy
%O 0,5
%A _N. J. A. Sloane_
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