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 A308986 #12 Aug 05 2025 10:34:12
%S A308986 1,-2,2,-4,10,-20,36,-72,154,-308,596,-1192,2420,-4840,9608,-19216,
%T A308986 38586,-77172,154036,-308072,616740,-1233480,2465768,-4931536,9865492,
%U A308986 -19730984,39457128,-78914256,157838120,-315676240,631333264,-1262666528,2525371642,-5050743284
%N A308986 Expansion of Product_{k>=0} 1/(1 + 2*x^(2^k)).
%C A308986 Convolution inverse of A001316.
%H A308986 Michael De Vlieger, <a href="/A308986/b308986.txt">Table of n, a(n) for n = 0..3322</a>
%H A308986 Ignas Gasparavičius, Andrius Grigutis, and Juozas Petkelis, <a href="https://arxiv.org/abs/2507.23619">Picturesque convolution-like recurrences and partial sums' generation</a>, arXiv:2507.23619 [math.NT], 2025. See p. 28.
%F A308986 a(0) = 1; a(n) = -Sum_{k=1..n} 2^A000120(k) * a(n-k).
%t A308986 nmax = 33; CoefficientList[Series[Product[1/(1 + 2 x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t A308986 a[0] = 1; a[n_] := a[n] = -Sum[2^DigitCount[k, 2, 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]
%Y A308986 Cf. A000120, A001316, A006046, A308985.
%K A308986 sign
%O A308986 0,2
%A A308986 _Ilya Gutkovskiy_, Jul 04 2019