A321183 a(n) = [x^((n*(n+1)/2)^2)] Product_{k=1..n} Sum_{m>=0} x^(k^2*m).

1, 1, 3, 26, 438, 11674, 434613, 21040885, 1263748763, 91057116368, 7676892453542, 742890018054927, 81267790173334794, 9926903213704358577, 1340280764681712515084, 198320073897808037293388, 31929177807445245255119558, 5558580993355817894674501169, 1040777481846356463369367882750

Offset: 0

Author

Seiichi Manyama, Oct 29 2018

Keywords

• nonn

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)^2.

Examples

			1^2* 0 + 2^2*0 + 3^2*4 = 36.
1^2* 0 + 2^2*9 + 3^2*0 = 36.
1^2* 1 + 2^2*2 + 3^2*3 = 36.
1^2* 2 + 2^2*4 + 3^2*2 = 36.
1^2* 3 + 2^2*6 + 3^2*1 = 36.
1^2* 4 + 2^2*8 + 3^2*0 = 36.
1^2* 5 + 2^2*1 + 3^2*3 = 36.
1^2* 6 + 2^2*3 + 3^2*2 = 36.
1^2* 7 + 2^2*5 + 3^2*1 = 36.
1^2* 8 + 2^2*7 + 3^2*0 = 36.
1^2* 9 + 2^2*0 + 3^2*3 = 36.
1^2*10 + 2^2*2 + 3^2*2 = 36.
1^2*11 + 2^2*4 + 3^2*1 = 36.
1^2*12 + 2^2*6 + 3^2*0 = 36.
1^2*14 + 2^2*1 + 3^2*2 = 36.
1^2*15 + 2^2*3 + 3^2*1 = 36.
1^2*16 + 2^2*5 + 3^2*0 = 36.
1^2*18 + 2^2*0 + 3^2*2 = 36.
1^2*19 + 2^2*2 + 3^2*1 = 36.
1^2*20 + 2^2*4 + 3^2*0 = 36.
1^2*23 + 2^2*1 + 3^2*1 = 36.
1^2*24 + 2^2*3 + 3^2*0 = 36.
1^2*27 + 2^2*0 + 3^2*1 = 36.
1^2*28 + 2^2*2 + 3^2*0 = 36.
1^2*32 + 2^2*1 + 3^2*0 = 36.
1^2*36 + 2^2*0 + 3^2*0 = 36.
So a(3) = 26.
		

Crossrefs

Cf. A000537, A037444, A321181, A321186.

Extensions

a(16)-a(18) from Alois P. Heinz, Oct 29 2018