%I #20 Sep 14 2021 16:20:52

%S 0,0,1,0,0,8,0,0,16,0,18,0,0,72,0,0,0,32,81,0,128,0,0,0,0,288,50,0,0,

%T 200,0,0,256,0,450,0,0,72,0,0,288,800,0,0,0,648,0,0,0,0,723,0,1152,

%U 392,0,0,0,0,882,0,0,1800,0,0,0,1696,0,0,512,0,0,0,1296,1152,2450,0,0,0,0,0,2048,0,162,0,0,4176,0,0,0,3200,1458

%N Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.

%H Seiichi Manyama, <a href="/A347801/b347801.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) is sum of i^2 * j^2 for positive integers i,j such that i^2+j^2=n.

%o (PARI) a(n) = sum(i=1, n, sum(j=1, n, (i^2+j^2==n)*(i*j)^2));

%o (PARI) my(N=99, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^2))

%Y Cf. A000404, A000925, A037214, A347802, A347803.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Sep 14 2021