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A101562 a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+4*x^k).

%I A101562 #13 Aug 31 2024 18:07:40
%S A101562 1,3,17,67,257,1011,4097,16451,65553,261891,1048577,4195379,16777217,
%T A101562 67104771,268435729,1073758275,4294967297,17179804659,68719476737,
%U A101562 274878168899,1099511631889,4398045462531,17592186044417,70368748389427
%N A101562 a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+4*x^k).
%H A101562 G. C. Greubel, <a href="/A101562/b101562.txt">Table of n, a(n) for n = 0..1000</a>
%F A101562 a(n) = Sum_{k=0..n} (-1)^(n-k) * 4^k * A051731(n+1, k+1).
%F A101562 a(n) = (-1)^n * Sum_{d|n+1} (-4)^(d-1). - _G. C. Greubel_, Jun 25 2024
%t A101562 A101562[n_]:= (-1)^n*DivisorSum[n+1, (-4)^(#-1) &];
%t A101562 Table[A101562[n], {n,0,40}] (* _G. C. Greubel_, Jun 25 2024 *)
%o A101562 (Magma)
%o A101562 A101562:= func< n | (&+[(-1)^(n-k)*4^k*0^((n+1) mod (k+1)): k in [0..n]]) >;
%o A101562 [A101562(n): n in [0..40]]; // _G. C. Greubel_, Jun 25 2024
%o A101562 (SageMath)
%o A101562 def A101562(n): return sum((-1)^(n+k)*4^k*0^((n+1)%(k+1)) for k in range(n+1))
%o A101562 [A101562(n) for n in range(41)] # _G. C. Greubel_, Jun 25 2024
%Y A101562 Cf. A048272, A051731, A081295, A101561, A101563.
%K A101562 easy,nonn
%O A101562 0,2
%A A101562 _Paul Barry_, Dec 07 2004