A321238 a(n) = [x^(n^3)] Product_{k=1..n} Sum_{m>=0} x^(k*m^2).
1, 1, 1, 4, 16, 87, 911, 8081, 82494, 1108584, 14559487, 206462480, 3300362073, 54235076625, 939612600043, 17366394088532, 332129019947772, 6615538793829307, 137564490944940832, 2954281836759475893, 65572183746807351880, 1503752010271535590284, 35476544827929325305961
Offset: 0
Keywords
Examples
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.
Programs
-
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)}
Comments