A265095 a(n) = Sum_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009).

1, 2, 3, 11, 27, 270, 4366, 82491, 1762107, 135979835, 10135979835, 753144350523, 130499482241148, 20953464347912316, 6242774737775732860, 2960555481288609431503, 1211886375095917784137679, 719537152598665509899534287, 851154233276178632011679465423

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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)) ~ q(n)^n.

Mathematica

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

Crossrefs

Cf. A259436, A265094.

Sequence in context: A295613 A232212 A232219 * A301804 A335856 A335816

Adjacent sequences: A265092 A265093 A265094 * A265096 A265097 A265098

Keyword

nonn

Author

Vaclav Kotesovec, Dec 01 2015

Status

approved