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%I #14 Oct 29 2018 11:38:43
%S 1,1,2,6,25,123,683,4083,25839,171324,1178755,8362768,60867478,
%T 452760486,3431366195,26430813268,206504120774,1633813641572,
%U 13071700375914,105635826348216,861408409243195,7081998941608535,58658594339423251,489168002223876023,4104791591982736028
%N a(n) = [x^(n*(n+1)*(2*n+1)/6)] Product_{k=1..n} Sum_{m>=0} x^(k^2*m).
%C Also the number of nonnegative integer solutions (a_1, a_2, ... , a_n) to the equation 1^2*a_1 + 2^2*a_2 + ... + n^2*a_n = n*(n+1)*(2*n+1)/6.
%H Seiichi Manyama, <a href="/A321186/b321186.txt">Table of n, a(n) for n = 0..36</a>
%e 1^2* 0 + 2^2*3 + 3^2*2 + 4^2*0 = 30.
%e 1^2* 1 + 2^2*1 + 3^2*1 + 4^2*1 = 30.
%e 1^2* 1 + 2^2*5 + 3^2*1 + 4^2*0 = 30.
%e 1^2* 2 + 2^2*3 + 3^2*0 + 4^2*1 = 30.
%e 1^2* 2 + 2^2*7 + 3^2*0 + 4^2*0 = 30.
%e 1^2* 3 + 2^2*0 + 3^2*3 + 4^2*0 = 30.
%e 1^2* 4 + 2^2*2 + 3^2*2 + 4^2*0 = 30.
%e 1^2* 5 + 2^2*0 + 3^2*1 + 4^2*1 = 30.
%e 1^2* 5 + 2^2*4 + 3^2*1 + 4^2*0 = 30.
%e 1^2* 6 + 2^2*2 + 3^2*0 + 4^2*1 = 30.
%e 1^2* 6 + 2^2*6 + 3^2*0 + 4^2*0 = 30.
%e 1^2* 8 + 2^2*1 + 3^2*2 + 4^2*0 = 30.
%e 1^2* 9 + 2^2*3 + 3^2*1 + 4^2*0 = 30.
%e 1^2*10 + 2^2*1 + 3^2*0 + 4^2*1 = 30.
%e 1^2*10 + 2^2*5 + 3^2*0 + 4^2*0 = 30.
%e 1^2*12 + 2^2*0 + 3^2*2 + 4^2*0 = 30.
%e 1^2*13 + 2^2*2 + 3^2*1 + 4^2*0 = 30.
%e 1^2*14 + 2^2*0 + 3^2*0 + 4^2*1 = 30.
%e 1^2*14 + 2^2*4 + 3^2*0 + 4^2*0 = 30.
%e 1^2*17 + 2^2*1 + 3^2*1 + 4^2*0 = 30.
%e 1^2*18 + 2^2*3 + 3^2*0 + 4^2*0 = 30.
%e 1^2*21 + 2^2*0 + 3^2*1 + 4^2*0 = 30.
%e 1^2*22 + 2^2*2 + 3^2*0 + 4^2*0 = 30.
%e 1^2*26 + 2^2*1 + 3^2*0 + 4^2*0 = 30.
%e 1^2*30 + 2^2*0 + 3^2*0 + 4^2*0 = 30.
%e So a(4) = 25.
%Y Cf. A037444, A321183.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 29 2018
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