A293465 - OEIS

%I #9 Oct 09 2017 19:17:46

%S 1,-1,3,-13,19,-77,179,-461,1075,-3021,7219,-17357,44083,-103373,

%T 257075,-627661,1469491,-3511245,8547379,-19764173,47344691,

%U -112038861,261254195,-611161037,1435659315,-3329070029,7743892531,-18025911245,41566759987,-95872193485

%N a(n) = Sum_{k=0..n} (-1)^k * 2^k * q(k), where q(k) is A000009 (partitions into distinct parts).

%H Vaclav Kotesovec, <a href="/A293465/b293465.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ (-1)^n * 2^(n-1) * exp(Pi*sqrt(n/3)) / (3^(5/4) * n^(3/4)).

%F a(n) ~ (-1)^n * 2/3 * 2^n * A000009(n).

%t Table[Sum[(-1)^k * 2^k * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]

%Y Cf. A025147, A293466.

%K sign

%O 0,3

%A _Vaclav Kotesovec_, Oct 09 2017