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G.f.: square root of theta series of lattice in A004535.
1

%I #12 Dec 11 2017 11:23:24

%S 1,0,126,1568,756,-165312,-1227240,19894464,414106686,-456317568,

%T -96106099320,-809737207776,15047550684488,345938324437440,

%U -318788546956992,-91256560218798912,-842108390970746508,15331399952805675648,380895013380314119302,-178390965727200705696

%N G.f.: square root of theta series of lattice in A004535.

%H Vaclav Kotesovec, <a href="/A109146/b109146.txt">Table of n, a(n) for n = 0..800</a>

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%t terms = 20; t2 = EllipticTheta[2, 0, q]; t3 = EllipticTheta[3, 0, q]; s = Sqrt[(t3^7 + 7*t3^3*t2^4)^2 + (t2^7 + 7*t2^3*t3^4)^2] + O[q]^terms // Normal; Join[{1, 0}, Rest[(List @@ s) /. q -> 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 08 2017 *)

%K sign

%O 0,3

%A _N. J. A. Sloane_ and _Nadia Heninger_, Aug 18 2005