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 A338695 #17 Apr 24 2021 09:58:14
%S A338695 1,4,12,34,80,204,448,1072,2308,5280,11264,25088,53248,116032,245920,
%T A338695 527880,1114112,2369152,4980736,10508880,22022336,46193664,96468992,
%U A338695 201469408,419430416,872734720,1811960832,3758844096,7784628224,16107909312,33285996544,68723417856,141734089728
%N A338695 a(n) = Sum_{d|n} 2^(d-1) * binomial(d, n/d).
%F A338695 G.f.: (1/2) * Sum_{k>=1} ( (2 + 2 * x^k)^k - 2^k ) = Sum_{k>=1} 2^(k-1) * ( (1 + x^k)^k - 1 ).
%F A338695 If p is prime, a(p) = p * 2^(p-1).
%t A338695 a[n_] := DivisorSum[n, 2^(# - 1) * Binomial[#, n/#] &]; Array[a, 20] (* _Amiram Eldar_, Apr 24 2021 *)
%o A338695 (PARI) a(n) = sumdiv(n, d, 2^(d-1)*binomial(d, n/d));
%o A338695 (PARI) N=40; x='x+O('x^N); Vec(sum(k=1, N, (2+2*x^k)^k-2^k)/2)
%Y A338695 Cf. A034729, A318636, A318637, A338694.
%K A338695 nonn
%O A338695 1,2
%A A338695 _Seiichi Manyama_, Apr 24 2021