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 A321239 a(n) = [x^(n^3)] Product_{k=1..n} Sum_{m>=0} x^(k^2*m). 1

%I

%S 1,1,3,16,141,1534,19111,262103,3853373,59763670,966945204,

%T 16191250596,278933800080,4921604827876,88627915588351,

%U 1624349874930925,30231112607904743,570284342486800214,10887435073866747752,210086404047975194316,4092940691144348506396,80432925119259253535963

%N a(n) = [x^(n^3)] 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^3.

%e 1^2* 0 + 2^2*0 + 3^2*3 = 27.

%e 1^2* 1 + 2^2*2 + 3^2*2 = 27.

%e 1^2* 2 + 2^2*4 + 3^2*1 = 27.

%e 1^2* 3 + 2^2*6 + 3^2*0 = 27.

%e 1^2* 5 + 2^2*1 + 3^2*2 = 27.

%e 1^2* 6 + 2^2*3 + 3^2*1 = 27.

%e 1^2* 7 + 2^2*5 + 3^2*0 = 27.

%e 1^2* 9 + 2^2*0 + 3^2*2 = 27.

%e 1^2*10 + 2^2*2 + 3^2*1 = 27.

%e 1^2*11 + 2^2*4 + 3^2*0 = 27.

%e 1^2*14 + 2^2*1 + 3^2*1 = 27.

%e 1^2*15 + 2^2*3 + 3^2*0 = 27.

%e 1^2*18 + 2^2*0 + 3^2*1 = 27.

%e 1^2*19 + 2^2*2 + 3^2*0 = 27.

%e 1^2*23 + 2^2*1 + 3^2*0 = 27.

%e 1^2*27 + 2^2*0 + 3^2*0 = 27.

%e So a(3) = 16.

%o (PARI) {a(n) = polcoeff(prod(i=1, n, sum(j=0, n^3\i^2, x^(i^2*j)+x*O(x^(n^3)))), n^3)}

%Y Cf. A001156, A321238.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 01 2018

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Last modified March 30 09:39 EDT 2023. Contains 361609 sequences. (Running on oeis4.)