This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259400 #12 Jun 25 2022 08:24:50
%S A259400 1,3,11,35,115,339,1043,2963,8595,23955,66963,181651,497043,1324435,
%T A259400 3536275,9303443,24442259,63370643,164296083,421197203,1078654355,
%U A259400 2739598739,6942291347,17469994387,43894109587,109593687443,273070880147,677066241427,1675109266835
%N A259400 a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041.
%C A259400 In general, Sum_{k=0..n} (m^k * p(k)) ~ m/(m-1) * m^n * p(n), for m > 1.
%F A259400 a(n) ~ 2^(n-1) * exp(Pi*sqrt(2*n/3)) / (n*sqrt(3)).
%t A259400 Table[Sum[2^k*PartitionsP[k],{k,0,n}],{n,0,40}]
%Y A259400 Cf. A000041, A000079, A259401.
%Y A259400 Partial sums of A327550.
%K A259400 nonn
%O A259400 0,2
%A A259400 _Vaclav Kotesovec_, Jun 26 2015