A321186 a(n) = [x^(n*(n+1)*(2*n+1)/6)] Product_{k=1..n} Sum_{m>=0} x^(k^2*m).

1, 1, 2, 6, 25, 123, 683, 4083, 25839, 171324, 1178755, 8362768, 60867478, 452760486, 3431366195, 26430813268, 206504120774, 1633813641572, 13071700375914, 105635826348216, 861408409243195, 7081998941608535, 58658594339423251, 489168002223876023, 4104791591982736028

Offset

0,3

Comments

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.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..36

Example

1^2* 0 + 2^2*3 + 3^2*2 + 4^2*0 = 30.
1^2* 1 + 2^2*1 + 3^2*1 + 4^2*1 = 30.
1^2* 1 + 2^2*5 + 3^2*1 + 4^2*0 = 30.
1^2* 2 + 2^2*3 + 3^2*0 + 4^2*1 = 30.
1^2* 2 + 2^2*7 + 3^2*0 + 4^2*0 = 30.
1^2* 3 + 2^2*0 + 3^2*3 + 4^2*0 = 30.
1^2* 4 + 2^2*2 + 3^2*2 + 4^2*0 = 30.
1^2* 5 + 2^2*0 + 3^2*1 + 4^2*1 = 30.
1^2* 5 + 2^2*4 + 3^2*1 + 4^2*0 = 30.
1^2* 6 + 2^2*2 + 3^2*0 + 4^2*1 = 30.
1^2* 6 + 2^2*6 + 3^2*0 + 4^2*0 = 30.
1^2* 8 + 2^2*1 + 3^2*2 + 4^2*0 = 30.
1^2* 9 + 2^2*3 + 3^2*1 + 4^2*0 = 30.
1^2*10 + 2^2*1 + 3^2*0 + 4^2*1 = 30.
1^2*10 + 2^2*5 + 3^2*0 + 4^2*0 = 30.
1^2*12 + 2^2*0 + 3^2*2 + 4^2*0 = 30.
1^2*13 + 2^2*2 + 3^2*1 + 4^2*0 = 30.
1^2*14 + 2^2*0 + 3^2*0 + 4^2*1 = 30.
1^2*14 + 2^2*4 + 3^2*0 + 4^2*0 = 30.
1^2*17 + 2^2*1 + 3^2*1 + 4^2*0 = 30.
1^2*18 + 2^2*3 + 3^2*0 + 4^2*0 = 30.
1^2*21 + 2^2*0 + 3^2*1 + 4^2*0 = 30.
1^2*22 + 2^2*2 + 3^2*0 + 4^2*0 = 30.
1^2*26 + 2^2*1 + 3^2*0 + 4^2*0 = 30.
1^2*30 + 2^2*0 + 3^2*0 + 4^2*0 = 30.
So a(4) = 25.

Crossrefs

Cf. A037444, A321183.

Sequence in context: A321720 A358499 A357949 * A291558 A357902 A370510

Adjacent sequences: A321183 A321184 A321185 * A321187 A321188 A321189

Keyword

nonn

Author

Seiichi Manyama, Oct 29 2018

Status

approved