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%I #15 Oct 24 2017 02:28:53
%S 2,-4,6,-12,16,-24,38,-52,74,-104,142,-192,258,-340,446,-584,756,-972,
%T 1244,-1580,1996,-2516,3148,-3924,4878,-6032,7434,-9136,11182,-13644,
%U 16608,-20148,24378,-29428,35422,-42540,50978,-60940,72700,-86556,102838,-121952,144360,-170564,201176,-236900,278494,-326876,383094,-448288,523824,-611248,712256,-828860,963324,-1118160,1296296,-1501028,1736030,-2005540
%N G.f.: 2*q * Product_{n>=1} (1 + q^(2*n))/((1 + q^n)*(1 + q^(2*n-1))*(1 + q^(4*n))) in powers of q.
%C G.f. of row 1 in rectangular array A292929.
%H Vaclav Kotesovec, <a href="/A293132/b293132.txt">Table of n, a(n) for n = 1..2000</a>
%F a(n) ~ -(-1)^n * 7^(1/4) * exp(sqrt(7*n/3)*Pi/2) / (2^(3/2) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Oct 23 2017
%e G.f.: A(q) = 2*q - 4*q^2 + 6*q^3 - 12*q^4 + 16*q^5 - 24*q^6 + 38*q^7 - 52*q^8 + 74*q^9 - 104*q^10 + 142*q^11 - 192*q^12 + 258*q^13 - 340*q^14 +...
%t nmax = 50; CoefficientList[Series[2*Product[1/((1 + x^(2*k-1))^2 * (1 + x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 23 2017 *)
%o (PARI) {a(n) = polcoeff( 2*q * prod(m=1,n, (1 + q^(2*m))/((1 + q^m)*(1 + q^(2*m-1))*(1 + q^(4*m)) +q*O(q^n))),n,q)}
%o for(n=1,60,print1(a(n),", "))
%Y Cf. A292929, A294065, A294066, A294067.
%K sign
%O 1,1
%A _Paul D. Hanna_, Oct 22 2017
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