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%I #22 Oct 29 2018 12:10:50
%S 1,1,3,26,438,11674,434613,21040885,1263748763,91057116368,
%T 7676892453542,742890018054927,81267790173334794,9926903213704358577,
%U 1340280764681712515084,198320073897808037293388,31929177807445245255119558,5558580993355817894674501169,1040777481846356463369367882750
%N a(n) = [x^((n*(n+1)/2)^2)] 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)^2.
%e 1^2* 0 + 2^2*0 + 3^2*4 = 36.
%e 1^2* 0 + 2^2*9 + 3^2*0 = 36.
%e 1^2* 1 + 2^2*2 + 3^2*3 = 36.
%e 1^2* 2 + 2^2*4 + 3^2*2 = 36.
%e 1^2* 3 + 2^2*6 + 3^2*1 = 36.
%e 1^2* 4 + 2^2*8 + 3^2*0 = 36.
%e 1^2* 5 + 2^2*1 + 3^2*3 = 36.
%e 1^2* 6 + 2^2*3 + 3^2*2 = 36.
%e 1^2* 7 + 2^2*5 + 3^2*1 = 36.
%e 1^2* 8 + 2^2*7 + 3^2*0 = 36.
%e 1^2* 9 + 2^2*0 + 3^2*3 = 36.
%e 1^2*10 + 2^2*2 + 3^2*2 = 36.
%e 1^2*11 + 2^2*4 + 3^2*1 = 36.
%e 1^2*12 + 2^2*6 + 3^2*0 = 36.
%e 1^2*14 + 2^2*1 + 3^2*2 = 36.
%e 1^2*15 + 2^2*3 + 3^2*1 = 36.
%e 1^2*16 + 2^2*5 + 3^2*0 = 36.
%e 1^2*18 + 2^2*0 + 3^2*2 = 36.
%e 1^2*19 + 2^2*2 + 3^2*1 = 36.
%e 1^2*20 + 2^2*4 + 3^2*0 = 36.
%e 1^2*23 + 2^2*1 + 3^2*1 = 36.
%e 1^2*24 + 2^2*3 + 3^2*0 = 36.
%e 1^2*27 + 2^2*0 + 3^2*1 = 36.
%e 1^2*28 + 2^2*2 + 3^2*0 = 36.
%e 1^2*32 + 2^2*1 + 3^2*0 = 36.
%e 1^2*36 + 2^2*0 + 3^2*0 = 36.
%e So a(3) = 26.
%Y Cf. A000537, A037444, A321181, A321186.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 29 2018
%E a(16)-a(18) from _Alois P. Heinz_, Oct 29 2018
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