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 A360802 #14 Aug 02 2023 02:00:15
%S A360802 1,3,5,17,17,105,65,449,641,1953,1025,16257,4097,37761,93185,247809,
%T A360802 65537,1499649,262145,6596609,8847361,13654017,4194305,210026497,
%U A360802 90177537,251764737,833880065,2659418113,268435457,18345328641,1073741825,53553922049,75438751745
%N A360802 Expansion of Sum_{k>0} (x / (1 - (2 * x)^k))^k.
%F A360802 a(n) = Sum_{d|n} 2^(n-d) * binomial(d+n/d-2,d-1).
%F A360802 If p is prime, a(p) = 1 + 2^(p-1).
%t A360802 a[n_] := DivisorSum[n, 2^(n-#) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* _Amiram Eldar_, Aug 02 2023 *)
%o A360802 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-(2*x)^k))^k))
%o A360802 (PARI) a(n) = sumdiv(n, d, 2^(n-d)*binomial(d+n/d-2, d-1));
%Y A360802 Cf. A157019, A339481.
%K A360802 nonn
%O A360802 1,2
%A A360802 _Seiichi Manyama_, Feb 21 2023