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A347801 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.

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%I A347801 #20 Sep 14 2021 16:20:52
%S A347801 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 A347801 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 A347801 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 A347801 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.
%H A347801 Seiichi Manyama, <a href="/A347801/b347801.txt">Table of n, a(n) for n = 0..10000</a>
%F A347801 a(n) is sum of i^2 * j^2 for positive integers i,j such that i^2+j^2=n.
%o A347801 (PARI) a(n) = sum(i=1, n, sum(j=1, n, (i^2+j^2==n)*(i*j)^2));
%o A347801 (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 A347801 Cf. A000404, A000925, A037214, A347802, A347803.
%K A347801 nonn
%O A347801 0,6
%A A347801 _Seiichi Manyama_, Sep 14 2021