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 A321238 a(n) = [x^(n^3)] Product_{k=1..n} Sum_{m>=0} x^(k*m^2). 1
 1, 1, 1, 4, 16, 87, 911, 8081, 82494, 1108584, 14559487, 206462480, 3300362073, 54235076625, 939612600043, 17366394088532, 332129019947772, 6615538793829307, 137564490944940832, 2954281836759475893, 65572183746807351880, 1503752010271535590284, 35476544827929325305961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also the number of nonnegative integer solutions (a_1, a_2, ... , a_n) to the equation a_1^2 + 2*a_2^2 + ... + n*a_n^2 = n^3. LINKS EXAMPLE 1*0^2 + 2*0^2 + 3*0^2 + 4*4^2 = 64. 1*0^2 + 2*0^2 + 3*4^2 + 4*2^2 = 64. 1*1^2 + 2*0^2 + 3*3^2 + 4*3^2 = 64. 1*1^2 + 2*4^2 + 3*3^2 + 4*1^2 = 64. 1*2^2 + 2*2^2 + 3*4^2 + 4*1^2 = 64. 1*2^2 + 2*4^2 + 3*2^2 + 4*2^2 = 64. 1*4^2 + 2*0^2 + 3*2^2 + 4*3^2 = 64. 1*4^2 + 2*0^2 + 3*4^2 + 4*0^2 = 64. 1*4^2 + 2*4^2 + 3*0^2 + 4*2^2 = 64. 1*4^2 + 2*4^2 + 3*2^2 + 4*1^2 = 64. 1*5^2 + 2*0^2 + 3*1^2 + 4*3^2 = 64. 1*5^2 + 2*2^2 + 3*3^2 + 4*1^2 = 64. 1*5^2 + 2*4^2 + 3*1^2 + 4*1^2 = 64. 1*6^2 + 2*0^2 + 3*2^2 + 4*2^2 = 64. 1*7^2 + 2*2^2 + 3*1^2 + 4*1^2 = 64. 1*8^2 + 2*0^2 + 3*0^2 + 4*0^2 = 64. So a(4) = 16. PROG (PARI) {a(n) = polcoeff(prod(i=1, n, sum(j=0, sqrtint(n^3\i), x^(i*j^2)+x*O(x^(n^3)))), n^3)} CROSSREFS Cf. A300446, A321139, A321239. Sequence in context: A184507 A165964 A300279 * A005618 A005495 A052124 Adjacent sequences: A321235 A321236 A321237 * A321239 A321240 A321241 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 01 2018 STATUS approved

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Last modified March 31 11:51 EDT 2023. Contains 361648 sequences. (Running on oeis4.)