A282474
Coefficients in q-expansion of E_4^8, where E_4 is the Eisenstein series A004009.
Original entry on oeis.org
1, 1920, 1630080, 803228160, 253366181760, 53205643249920, 7498254194403840, 699684356363412480, 42100628403784982400, 1614922125605880493440, 42332208491309728078080, 812648422343847344279040, 12060223533365891970132480
Offset: 0
-
terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^8 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
A299955
Coefficients in expansion of E_4^(3/2).
Original entry on oeis.org
1, 360, 24840, -465120, 57417480, -6800282640, 930889890720, -139401582644160, 22250341370421000, -3723955494287559480, 646515765251485521840, -115559140273640812421280, 21150946022800731753255840, -3948247836773858791840263120
Offset: 0
E_4^(k/8):
A108091 (k=1),
A289307 (k=2),
A289308 (k=3),
A289292 (k=4),
A289309 (k=5),
A289318 (k=6),
A289319 (k=7),
A004009 (k=8), this sequence (k=12),
A008410 (k=16),
A008411 (k=24),
A282012 (k=32),
A282015 (k=40).
A004670
Theta series of extremal even unimodular lattice in dimension 32.
Original entry on oeis.org
1, 0, 146880, 64757760, 4844836800, 137695887360, 2121555283200, 21421110804480, 158757684004800, 928986331545600, 4512164186816640, 18847854517248000, 69519016873985280, 230952108679004160
Offset: 0
G.f.: 1 + 146880*q^2 + 64757760*q^3 + 4844836800*q^4 + ...
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 195.
- Andy Huchala, Table of n, a(n) for n = 0..20000
- N. Elkies, Rational Lattices and their Theta Functions
- N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
- G. Nebe and N. J. A. Sloane, Home page for this lattice
- Index entries for sequences related to Barnes-Wall lattices
-
e4 = eisenstein_series_qexp(4,20,normalization = "integral");
delta = CuspForms(1,12).0.q_expansion(20);
(e4^4 - 960*delta*e4).list()[:20] # Andy Huchala, May 01 2021
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