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 A360801 #15 Aug 02 2023 02:00:12
%S A360801 1,3,5,13,17,51,65,169,281,603,1025,2373,4097,8655,16685,33969,65537,
%T A360801 134151,262145,530269,1050481,2108439,4194305,8420201,16778337,
%U A360801 33607707,67120565,134338493,268435457,537151131,1073741825,2148024289,4295035145,8591048739
%N A360801 Expansion of Sum_{k>0} (x / (1 - 2 * x^k))^k.
%F A360801 a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d+n/d-2,d-1).
%F A360801 If p is prime, a(p) = 1 + 2^(p-1).
%t A360801 a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* _Amiram Eldar_, Aug 02 2023 *)
%o A360801 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-2*x^k))^k))
%o A360801 (PARI) a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d+n/d-2, d-1));
%Y A360801 Cf. A157019, A217670, A324158.
%K A360801 nonn
%O A360801 1,2
%A A360801 _Seiichi Manyama_, Feb 21 2023