A304990 Squares of number of partitions into distinct parts.
1, 1, 1, 4, 4, 9, 16, 25, 36, 64, 100, 144, 225, 324, 484, 729, 1024, 1444, 2116, 2916, 4096, 5776, 7921, 10816, 14884, 20164, 27225, 36864, 49284, 65536, 87616, 115600, 152100, 200704, 262144, 342225, 446224, 577600, 746496, 964324, 1238769, 1587600
Offset: 0
Keywords
Programs
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Mathematica
Table[PartitionsQ[n]^2, {n, 0, 50}]
Formula
a(n) ~ exp(2*Pi*sqrt(n/3)) / (16*sqrt(3)*n^(3/2)).
a(n) = A000009(n)^2.
a(n) = [(x*y)^n] Product_{k>=1} (1 + x^k) * (1 + y^k). - Ilya Gutkovskiy, Apr 24 2025