%I #17 Sep 08 2022 08:44:48
%S 1,0,10668,317952,3747430,24569856,117503960,428990464,1355705388,
%T 3631734784,9033649880,19996626432,42549627976,82713667584,
%U 157758704304,279165280256,490745951846,808950325248,1335670719108,2081937198592,3270650346456,4874720530432
%N Theta series of laminated lattice LAMBDA_19.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 174.
%H Andy Huchala, <a href="/A023941/b023941.txt">Table of n, a(n) for n = 0..20000</a>
%e G.f.: 1 + 10668*q^4 + 317952*q^6 + 3747430*q^8 + 24569856*q^10 + 117503960*q^12 + ...
%o (Magma) L:=Lattice("Lambda",19); T<q> := ThetaSeries(L,12); T;
%o (Magma)
%o L := Lattice("Lambda",19);
%o B := Basis(ThetaSeriesModularFormSpace(L),30);
%o S := [1, 0, 10668, 317952, 3747430, 24569856, 117503960, 428990464, 1355705388, 3631734784, 9033649880, 19996626432, 42549627976, 82713667584, 157758704304, 279165280256, 490745951846, 808950325248, 1335670719108, 2081937198592];
%o Coefficients(&+[B[i] * S[i] : i in [1..20]]); // _Andy Huchala_, Jun 17 2021
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Andy Huchala_, Jun 17 2021