%I #20 Feb 03 2024 10:15:13

%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,2,62,0,0,268,356,0,0,2287,1130,0,

%T 0,5317,36879,0,0,203016,319415,0,0,2124580,1631750,0,0,10953868,

%U 41280525,0,0,242899218,472958485,0,0,2984270739,3419746788,0,0

%N a(n) is the number of ways the set {1^3, 2^3, ..., n^3} can be partitioned into two sets of equal sums.

%C a(n)=0 when n == 1 or 2 mod 4.

%H Alois P. Heinz and Ray Chandler, <a href="/A113263/b113263.txt">Table of n, a(n) for n = 1..130</a> (first 100 terms from Alois P. Heinz)

%F a(n) is half the coefficient of x^0 in product(x^(k^3)+x^(k^-3), k=1..n).

%F a(n) = [x^(n^3)] Product_{k=1..n-1} (x^(k^3) + 1/x^(k^3)). - _Ilya Gutkovskiy_, Feb 01 2024

%p A113263:=proc(n) local i,p,t; t:= NULL; p:=1; for i to n do p:=p*(x^(i^3)+x^(-i^3)); t:=t,coeff(p,x,0)/2; od; t; end;

%t p = 1; t = {}; Do[p = Expand[p(x^(n^3) + x^(-n^3))]; AppendTo[t, Select[ p, NumberQ[ # ] &]/2], {n, 56}]; t (* _Robert G. Wilson v_ *)

%Y Cf. A058498, A083527.

%K nonn

%O 1,15

%A _Floor van Lamoen_, Oct 21 2005

%E More terms from _Robert G. Wilson v_ and _Tony Noe_, Oct 27 2005