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

0,4

Links

Table of n, a(n) for n=0..41.

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

Mathematica

Table[PartitionsQ[n]^2, {n, 0, 50}]

Crossrefs

Cf. A000009, A000290, A001255.

Sequence in context: A319435 A226096 A071567 * A263727 A133037 A061886

Adjacent sequences: A304987 A304988 A304989 * A304991 A304992 A304993

Keyword

nonn

Author

Vaclav Kotesovec, May 23 2018

Status

approved