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%I #15 Oct 23 2017 12:18:31
%S 2,-4,8,-12,24,-32,64,-68,152,-120,392,-124,1000,320,3056,2836,10280,
%T 15112,38668,68348,154152,297948,633352,1269884,2649892,5395272,
%U 11157512,22890976,47251564,97224304,200605456,413622556,853809232,1762332664,3640315888,7521114700,15545862696,32142131064,66481012488,137544496052
%N Limit of rows in rectangular array A292929.
%C The g.f. of A292929 is R(x,q) = sqrt( Q(x,q) / Q(x,-q) ), where Q(x,q) = Sum_{n=-oo..+oo} (x - q^n)^n; the g.f. of this sequence equals the limit of the coefficient of x^n in R(x,q) / q^n as a power series in q.
%C a(n+1)/a(n) tends to 2.0946... - _Vaclav Kotesovec_, Oct 23 2017
%H Paul D. Hanna, <a href="/A293601/b293601.txt">Table of n, a(n) for n = 0..200</a>
%F G.f.: A(q) = 2 - 4*q + 8*q^2 - 12*q^3 + 24*q^4 - 32*q^5 + 64*q^6 - 68*q^7 + 152*q^8 - 120*q^9 + 392*q^10 - 124*q^11 + 1000*q^12 + 320*q^13 + 3056*q^14 + 2836*q^15 + 10280*q^16 + 15112*q^17 + 38668*q^18 +...
%F Let R(x,q) be the g.f. of A292929, then we can illustrate the g.f. of this sequence as follows.
%F The coefficient of x^4 in R(x,q) begins:
%F 2*q^4 - 4*q^5 + 8*q^6 - 12*q^7 + 24*q^8 - 40*q^9 + 38*q^10 +...
%F The coefficient of x^5 in R(x,q) begins:
%F 2*q^5 - 4*q^6 + 8*q^7 - 12*q^8 + 24*q^9 - 32*q^10 + 48*q^11 +...
%F The coefficient of x^6 in R(x,q) begins:
%F 2*q^6 - 4*q^7 + 8*q^8 - 12*q^9 + 24*q^10 - 32*q^11 + 64*q^12 +...
%F The g.f. A(q) equals the limit of the coefficient if x^n in R(x,q)/q^n.
%Y Cf. A292929.
%K sign
%O 0,1
%A _Paul D. Hanna_, Oct 22 2017
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