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%I #18 Sep 14 2021 15:01:53
%S 0,0,0,1,0,0,12,0,0,48,0,27,64,0,216,0,0,432,48,243,0,384,972,0,768,0,
%T 864,804,0,3456,600,0,0,1968,3888,1350,3072,0,5508,0,0,7776,2400,6075,
%U 1728,9600,1944,0,4096,7776,21600,2022,0,3456,17424,0,13824,21552,0,19521,0,31104,15984,0,0,21600,34896,11907
%N Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^3.
%H Seiichi Manyama, <a href="/A347802/b347802.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) is sum of i^2 * j^2 * k^2 for positive integers i,j,k such that i^2+j^2+k^2=n.
%o (PARI) a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, (i^2+j^2+k^2==n)*(i*j*k)^2)));
%o (PARI) my(N=66, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^3))
%Y Cf. A000408, A002102, A037215, A347801, A347803.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Sep 14 2021