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 A293464 a(n) = Sum_{k=0..n} (-1)^k * 2^k * p(k), where p(k) is the partition function A000041. 1

%I

%S 1,-1,7,-17,63,-161,543,-1377,4255,-11105,31903,-82785,232607,-594785,

%T 1617055,-4150113,10988703,-27939681,72985759,-183915361,473541791,

%U -1187402593,3015290015,-7512413025,18911702175,-46787875681,116689317023,-287306044257

%N a(n) = Sum_{k=0..n} (-1)^k * 2^k * p(k), where p(k) is the partition function A000041.

%H Vaclav Kotesovec, <a href="/A293464/b293464.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) ~ (-1)^n * 2/3 * 2^n * A000041(n).

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

%Y Cf. A087787, A259400.

%K sign

%O 0,3

%A _Vaclav Kotesovec_, Oct 09 2017

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)