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%I #9 Jun 25 2024 19:26:18
%S 1,3,17,67,257,1011,4097,16451,65553,261891,1048577,4195379,16777217,
%T 67104771,268435729,1073758275,4294967297,17179804659,68719476737,
%U 274878168899,1099511631889,4398045462531,17592186044417,70368748389427
%N a(n) = (-1)^n * coefficient of x^n in Sum_{k>=1} x^(k-1)/(1+4*x^k)}.
%H G. C. Greubel, <a href="/A101562/b101562.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * 4^k * A051731(n+1, k+1).
%F a(n) = (-1)^n * Sum_{d|n+1} (-4)^(d-1). - _G. C. Greubel_, Jun 25 2024
%t A101562[n_]:= (-1)^n*DivisorSum[n+1, (-4)^(#-1) &];
%t Table[A101562[n], {n,0,40}] (* _G. C. Greubel_, Jun 25 2024 *)
%o (Magma)
%o A101562:= func< n | (&+[(-1)^(n-k)*4^k*0^((n+1) mod (k+1)): k in [0..n]]) >;
%o [A101562(n): n in [0..40]]; // _G. C. Greubel_, Jun 25 2024
%o (SageMath)
%o def A101562(n): return sum((-1)^(n+k)*4^k*0^((n+1)%(k+1)) for k in range(n+1))
%o [A101562(n) for n in range(41)] # _G. C. Greubel_, Jun 25 2024
%Y Cf. A048272, A051731, A081295, A101561, A101563.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 07 2004
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