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 A360771 #15 Aug 02 2023 02:00:02
%S A360771 1,2,5,8,20,32,77,128,288,518,1104,2048,4313,8192,16832,32848,66568,
%T A360771 131072,264688,524288,1053737,2097824,4205568,8388608,16803744,
%U A360771 33554442,67162112,134222336,268550704,536870912,1073999165,2147483648,4295493376,8589962752
%N A360771 Expansion of Sum_{k>=0} (x * (2 + x^k))^k.
%F A360771 a(n) = Sum_{d|n} 2^(d-n/d+1) * binomial(d,n/d-1) for n > 0.
%F A360771 If p is an odd prime, a(p) = 2^p.
%t A360771 a[n_] := DivisorSum[n, 2^(# - n/# + 1) * Binomial[#, n/# - 1] &]; a[0] = 1; Array[a, 30, 0] (* _Amiram Eldar_, Aug 02 2023 *)
%o A360771 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x*(2+x^k))^k))
%o A360771 (PARI) a(n) = if(n==0, 1, sumdiv(n, d, 2^(d-n/d+1)*binomial(d, n/d-1)));
%Y A360771 Cf. A217668, A260148.
%K A360771 nonn
%O A360771 0,2
%A A360771 _Seiichi Manyama_, Feb 20 2023