%I #19 Jun 16 2021 21:43:48
%S 1,6,-48,672,-10686,185472,-3398304,64606080,-1261584768,25141699590,
%T -509112525600,10443131883360,-216500232587520,4528450460408448,
%U -95438941858567104,2024550297637849728,-43190698219545864702,925997705081213764608,-19940633776083900614736,431091393800371703940576
%N Coefficients of series whose 4th power is the theta series of D_4 (see A004011).
%D N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.
%H Vaclav Kotesovec, <a href="/A108092/b108092.txt">Table of n, a(n) for n = 0..730</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.
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/g4g7.pdf">Seven Staggering Sequences</a>.
%H N. J. A. Sloane, <a href="/A108092/a108092.pdf">Old and New Problems from 55 Years of the OEIS</a>, Slides of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, October 10 2019.
%F a(n) ~ -(-1)^n * Gamma(1/4)^3 * exp(Pi*n) / (2^(15/4) * Pi^(5/2) * n^(5/4)). - _Vaclav Kotesovec_, Dec 10 2017
%e More precisely, the theta series of D_4 begins 1 + 24*q^2 + 24*q^4 + 96*q^6 + 24*q^8 + 144*q^10 + 96*q^12 + ... and its 4th root is 1 + 6*q^2 - 48*q^4 + 672*q^6 - 10686*q^8 + 185472*q^10 - 3398304*q^12 + ...
%t CoefficientList[Series[(EllipticTheta[3,0,x]^4 + EllipticTheta[2,0,x]^4)^(1/4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Dec 10 2017 *)
%Y Cf. A004011, A108096.
%K sign
%O 0,2
%A _N. J. A. Sloane_ and _Michael Somos_, Jun 06 2005