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

0,4

Links

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

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)).

Mathematica

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

Crossrefs

Cf. A133018.

Sequence in context: A322342 A132377 A276978 * A285060 A371009 A369646

Adjacent sequences: A265091 A265092 A265093 * A265095 A265096 A265097

Keyword

nonn

Author

Vaclav Kotesovec, Dec 01 2015

Status

approved