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A002519 Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4. 3
1, 0, 0, 1728, 106472, 1734912, 19335168, 141575552, 805208040, 3725209088, 14647517184, 50579062848, 156715230240, 443680116992, 1162915024896, 2851005884544, 6596700471272, 14509559545344, 30507866603520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

R. Bacher and B. B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.

FORMULA

t3^28-56*t3^20*D8+280*t3^12*D8^2-512*t3^4*D8^3 where t3=theta3(z) and D8=(theta2(z)theta4(z))^4/16.

MATHEMATICA

terms = 19; t2 = EllipticTheta[2, 0, z]; t3 = EllipticTheta[3, 0, z]; t4 = EllipticTheta[4, 0, z]; D8 = (t2*t4)^4/16; s = t3^28 - 56*t3^20*D8 + 280*t3^12*D8^2 - 512*t3^4*D8^3 + O[z]^terms; CoefficientList[s, z] (* Jean-François Alcover, Jul 06 2017 *)

CROSSREFS

Cf. A002520.

Sequence in context: A017523 A237490 A223324 * A052068 A289210 A289209

Adjacent sequences:  A002516 A002517 A002518 * A002520 A002521 A002522

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000

STATUS

approved

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Last modified January 17 00:58 EST 2021. Contains 340213 sequences. (Running on oeis4.)