A265094 a(n) = q(n)^n, where q(n) = partition numbers into distinct parts (A000009).

1, 1, 1, 8, 16, 243, 4096, 78125, 1679616, 134217728, 10000000000, 743008370688, 129746337890625, 20822964865671168, 6221821273427820544, 2954312706550833698643, 1208925819614629174706176, 718325266223569592115396608, 850434696123579966501779931136

Offset: 0

Author

Vaclav Kotesovec, Dec 01 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Crossrefs

Cf. A133018.

Programs

Mathematica

Table[PartitionsQ[n]^n,{n,0,20}]

Formula

a(n) ~ exp(n^(3/2)*Pi/sqrt(3) + (Pi/(48*sqrt(3)) - 3*sqrt(3)/(8*Pi))*sqrt(n) - 1/32 - 9/(16*Pi^2)) / (3^(n/4) * 4^n * n^(3*n/4)).