A317577 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.

0, 0, 0, 0, 6, 6, 0, 18, 54, 0, 258, 612, 0, 3570, 8880, 0, 55764, 142368, 0, 947946, 2468844, 0, 17099808, 45375498, 0, 323927184, 871038570, 0, 6369199908, 17312303760

Offset: 1

Author

Ovidiu Bagdasar, Jul 31 2018

Keywords

• nonn
• easy

Comments

Constant term of Product_{k=1..n} (x^k+y^k+1/(x*y)^k).

Examples

			For n = 1, 2, 3, 4, a(n) = 0, as n*(n+1)/2 is not divisible by 3.
For n = 5, a(5) = 6, as {1,2,3,4,5} = {1,4}U{2,3}U{5} and there are 6 permutations.
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.
		

Links

• D. Andrica and O. Bagdasar, Some remarks on 3-partitions of multisets, Electron. Notes Discrete Math., TCDM'18 (2018).

Crossrefs

Cf. A112972.

Formula

a(n) = 6*A112972(n).