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%I #16 Sep 14 2021 17:33:19
%S 0,0,0,0,1,0,0,16,0,0,96,0,36,256,0,432,256,0,1728,64,486,2304,768,
%T 3888,0,3072,7776,1728,7112,0,13824,12864,0,27648,6336,15552,9261,
%U 18688,62208,21744,24576,0,72576,51456,24300,117504,38400,101088,9216,93184,155520,86400,142382,62208,352512,67344,0,202752,286176
%N Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^4.
%H Seiichi Manyama, <a href="/A347803/b347803.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) is sum of i^2 * j^2 * k^2 *m^2 for positive integers i,j,k,m such that i^2+j^2+k^2+m^2=n.
%o (PARI) a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, sum(m=1, n, (i^2+j^2+k^2+m^2==n)*(i*j*k*m)^2))));
%o (PARI) my(N=66, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^4))
%Y Cf. A000414, A014110, A037216, A347801, A347802.
%K nonn
%O 0,8
%A _Seiichi Manyama_, Sep 14 2021
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