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 A259400 a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041. 3

%I

%S 1,3,11,35,115,339,1043,2963,8595,23955,66963,181651,497043,1324435,

%T 3536275,9303443,24442259,63370643,164296083,421197203,1078654355,

%U 2739598739,6942291347,17469994387,43894109587,109593687443,273070880147,677066241427,1675109266835

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

%C In general, Sum_{k=0..n} (m^k * p(k)) ~ m/(m-1) * m^n * p(n), for m > 1.

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

%t Table[Sum[2^k*PartitionsP[k],{k,0,n}],{n,0,40}]

%Y Cf. A000041, A000079, A259401.

%Y Partial sums of A327550.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jun 26 2015

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Last modified March 30 04:12 EDT 2023. Contains 361603 sequences. (Running on oeis4.)