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%I #21 Jan 22 2024 15:24:35
%S 1,3,13,65,403,2669,18759,136477,1020373,7785741,60395165,474817833,
%T 3775005799,30298719855,245167429681,1997854542163,16381233095985,
%U 135050690760831,1118800428892925,9308791880014333,77755512086256649
%N Number of solutions to e(1)*1 + e(2)*2 + ... + e(n)*n = e(-1)*1 + e(-2)*2 + ... + e(-n)*n, where e(j) are from {-1,0,1}, j=-n,...,n.
%C a(n) = coefficient of x^(n*(n+1)) in the polynomial Product_{k=1..n} (1 + x^k + x^(2*k))^2, and is the maximal such coefficient as well.
%H Ray Chandler, <a href="/A156181/b156181.txt">Table of n, a(n) for n = 0..1052</a> (terms < 10^1000)
%H Steven R. Finch, <a href="/A000980/a000980.pdf">Signum equations and extremal coefficients</a>, February 7, 2009. [Cached copy, with permission of the author]
%F a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^2. - _Ilya Gutkovskiy_, Jan 22 2024
%t Table[Coefficient[Expand[Product[(1 + x^k + x^(2*k))^2, {k, 1, n}]],x, n*(n + 1)], {n, 0, 20}]
%Y Cf. A007576, A047653, A063865.
%K nonn
%O 0,2
%A _Steven Finch_, Feb 05 2009
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