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A265095 a(n) = Sum_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009). 1
1, 2, 3, 11, 27, 270, 4366, 82491, 1762107, 135979835, 10135979835, 753144350523, 130499482241148, 20953464347912316, 6242774737775732860, 2960555481288609431503, 1211886375095917784137679, 719537152598665509899534287, 851154233276178632011679465423 (list; graph; refs; listen; history; text; internal format)
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: A002981 A232212 A232219 * A235474 A075641 A176316

Adjacent sequences:  A265092 A265093 A265094 * A265096 A265097 A265098

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 01 2015

STATUS

approved

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Last modified May 24 03:21 EDT 2017. Contains 286937 sequences.