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

Author

Vaclav Kotesovec, Dec 01 2015

Keywords

• nonn

Crossrefs

Cf. A259436, A265094.

Programs

Mathematica

Table[Sum[PartitionsQ[k]^k, {k,0,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)) ~ q(n)^n.