A321181 a(n) = [x^((n*(n+1)/2)^2)] Product_{k=1..n} Sum_{m>=0} x^(k*m^2).

1, 1, 2, 7, 28, 262, 3428, 52289, 1147221, 30161625, 893291633, 30894822277, 1214415301634, 52617692115135, 2528123847871538, 133088227043557512, 7574733515354756765, 466116310963215784930, 30810712157925101729430, 2173319693639115252360852, 163247410881483617710298406

Offset

0,3

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*(n+1)/2)^2.

Links

Table of n, a(n) for n=0..20.

Example

1* 0^2 + 2*0^2 + 3*0^2 + 4*5^2 = 100.
1* 0^2 + 2*6^2 + 3*2^2 + 4*2^2 = 100.
1* 1^2 + 2*2^2 + 3*3^2 + 4*4^2 = 100.
1* 1^2 + 2*2^2 + 3*5^2 + 4*2^2 = 100.
1* 1^2 + 2*4^2 + 3*1^2 + 4*4^2 = 100.
1* 1^2 + 2*6^2 + 3*3^2 + 4*0^2 = 100.
1* 2^2 + 2*4^2 + 3*0^2 + 4*4^2 = 100.
1* 2^2 + 2*4^2 + 3*4^2 + 4*2^2 = 100.
1* 3^2 + 2*0^2 + 3*3^2 + 4*4^2 = 100.
1* 3^2 + 2*0^2 + 3*5^2 + 4*2^2 = 100.
1* 3^2 + 2*6^2 + 3*1^2 + 4*2^2 = 100.
1* 4^2 + 2*0^2 + 3*4^2 + 4*3^2 = 100.
1* 4^2 + 2*2^2 + 3*2^2 + 4*4^2 = 100.
1* 4^2 + 2*4^2 + 3*4^2 + 4*1^2 = 100.
1* 4^2 + 2*6^2 + 3*2^2 + 4*0^2 = 100.
1* 5^2 + 2*0^2 + 3*5^2 + 4*0^2 = 100.
1* 5^2 + 2*2^2 + 3*1^2 + 4*4^2 = 100.
1* 5^2 + 2*4^2 + 3*3^2 + 4*2^2 = 100.
1* 5^2 + 2*6^2 + 3*1^2 + 4*0^2 = 100.
1* 6^2 + 2*0^2 + 3*0^2 + 4*4^2 = 100.
1* 6^2 + 2*0^2 + 3*4^2 + 4*2^2 = 100.
1* 7^2 + 2*2^2 + 3*3^2 + 4*2^2 = 100.
1* 7^2 + 2*4^2 + 3*1^2 + 4*2^2 = 100.
1* 8^2 + 2*0^2 + 3*0^2 + 4*3^2 = 100.
1* 8^2 + 2*2^2 + 3*2^2 + 4*2^2 = 100.
1* 8^2 + 2*4^2 + 3*0^2 + 4*1^2 = 100.
1* 9^2 + 2*0^2 + 3*1^2 + 4*2^2 = 100.
1*10^2 + 2*0^2 + 3*0^2 + 4*0^2 = 100.
So a(4) = 28.

Crossrefs

Cf. A000122, A000537, A300446, A320932.

Sequence in context: A013011 A013181 A191478 * A122118 A337429 A059803

Adjacent sequences: A321178 A321179 A321180 * A321182 A321183 A321184

Keyword

nonn

Author

Seiichi Manyama, Oct 29 2018

Extensions

a(17)-a(20) from Alois P. Heinz, Oct 29 2018

Status

approved