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 A380652 #10 Feb 11 2025 16:36:56
%S A380652 1,1,0,-1,-1,-2,-1,1,4,3,-1,-4,-1,-3,0,5,5,4,-1,-5,-2,-5,-1,6,9,1,-6,
%T A380652 -5,13,14,11,1,-38,-39,-1,38,41,81,42,-37,-163,-128,37,167,56,143,11,
%U A380652 -214,-253,-219,36,257,149,328,105,-303,-624,-247,313,490,-455,-387,-476,-417,1251,1250
%N A380652 Shifts left one place under the inverse modulo 2 binomial transform.
%F A380652 a(0) = 1; a(n) = Sum_{k=0..n-1} (-1)^A010060(k) * (binomial(n-1,k) mod 2) * a(n-k-1).
%t A380652 a[0] = 1; a[n_] := a[n] = Sum[(-1)^ThueMorse[k] Mod[Binomial[n - 1, k], 2] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 65}]
%o A380652 (Python)
%o A380652 from functools import lru_cache
%o A380652 @lru_cache(maxsize=None)
%o A380652 def A380652(n): return sum((-A380652(n-k-1) if k.bit_count()&1 else A380652(n-k-1)) for k in range(n) if not (k&~(n-1))) if n else 1 # _Chai Wah Wu_, Feb 11 2025
%Y A380652 Cf. A000587, A010060, A047999, A166966.
%K A380652 sign
%O A380652 0,6
%A A380652 _Ilya Gutkovskiy_, Jan 29 2025