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A181722 Numerator of (1/n - Bernoulli number A164555(n)/A027642(n)).

%I A181722 #19 Mar 26 2024 04:11:32
%S A181722 0,0,1,1,7,1,5,1,13,1,1,1,901,1,-11,1,3647,1,-43825,1,1222387,1,
%T A181722 -854507,1,1181821001,1,-76977925,1,23749461059,1,-8615841275543,1,
%U A181722 28267510484519,1
%N A181722 Numerator of (1/n - Bernoulli number A164555(n)/A027642(n)).
%C A181722 An autosequence is a sequence whose inverse binomial transform is the sequence signed. In integers, the oldest example is Fibonacci A000045. In fractions, A164555/A027642 is the son of 1/n via the Akiyama-Tanigawa algorithm; grandson is (A174110/A174111) = 1/2, 2/3, 1/2, 2/15, ...; see A164020. See A174341/A174342. All are from the same family.
%H A181722 G. C. Greubel, <a href="/A181722/b181722.txt">Table of n, a(n) for n = 1..625</a>
%H A181722 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>.
%e A181722 Fractions are 0, 0, 1/6, 1/4, 7/30, 1/6, 5/42, 1/8, 13/90, 1/10, 1/66, 1/12, 901/2730, ...
%t A181722 a[n_] := If[n <= 2, 0, Numerator[1/n - BernoulliB[n-1]]];
%t A181722 Table[a[n], {n, 1, 34}] (* _Jean-François Alcover_, Jun 07 2017 *)
%o A181722 (Magma)
%o A181722 A181722:= func< n | n le 2 select 0 else Numerator(1/n - Bernoulli(n-1)) >;
%o A181722 [A181722(n): n in [1..40]]; // _G. C. Greubel_, Mar 25 2024
%o A181722 (SageMath)
%o A181722 def A181722(n): return 0 if n<3 else numerator(1/n - bernoulli(n-1))
%o A181722 [A181722(n) for n in range(1,41)] # _G. C. Greubel_, Mar 25 2024
%Y A181722 Cf. A000045, A027642, A164020, A164555, A174110, A174111, A174341, A174342.
%K A181722 sign,frac
%O A181722 1,5
%A A181722 _Paul Curtz_, Nov 17 2010