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%I #19 Jan 12 2020 11:26:05
%S 0,0,0,0,6,6,0,18,54,0,258,612,0,3570,8880,0,55764,142368,0,947946,
%T 2468844,0,17099808,45375498,0,323927184,871038570,0,6369199908,
%U 17312303760
%N Number of ways the set {1,2,...,n} can be split into three subsets X, Y, Z of equal sums, where the order of X, Y, Z matters.
%C Constant term of Product_{k=1..n} (x^k+y^k+1/(x*y)^k).
%H D. Andrica and O. Bagdasar, <a href="https://doi.org/10.1016/j.endm.2018.11.001">Some remarks on 3-partitions of multisets</a>, Electron. Notes Discrete Math., TCDM'18 (2018).
%F a(n) = 6*A112972(n).
%e For n = 1, 2, 3, 4, a(n) = 0, as n*(n+1)/2 is not divisible by 3.
%e For n = 5, a(5) = 6, as {1,2,3,4,5} = {1,4}U{2,3}U{5} and there are 6 permutations.
%e For n = 6, a(6) = 6, as {1,2,3,4,5,6} = {1,6}U{2,5}U{3,4} and there are 6 permutations.
%Y Cf. A112972.
%K nonn,easy
%O 1,5
%A _Ovidiu Bagdasar_, Jul 31 2018
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