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

0, 0, 1, 1, 7, 1, 5, 1, 13, 1, 1, 1, 901, 1, -11, 1, 3647, 1, -43825, 1, 1222387, 1, -854507, 1, 1181821001, 1, -76977925, 1, 23749461059, 1, -8615841275543, 1, 28267510484519, 1

Offset: 1

Author

Paul Curtz, Nov 17 2010

Keywords

• sign
• frac

Comments

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.

Examples

			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, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..625
• OEIS Wiki, Autosequence.

Crossrefs

Cf. A000045, A027642, A164020, A164555, A174110, A174111, A174341, A174342.

Programs

Magma

A181722:= func< n | n le 2 select 0 else Numerator(1/n - Bernoulli(n-1)) >;
[A181722(n): n in [1..40]]; // G. C. Greubel, Mar 25 2024

Mathematica

a[n_] := If[n <= 2, 0, Numerator[1/n - BernoulliB[n-1]]];
Table[a[n], {n, 1, 34}] (* Jean-François Alcover, Jun 07 2017 *)

SageMath

def A181722(n): return 0 if n<3 else numerator(1/n - bernoulli(n-1))
[A181722(n) for n in range(1,41)] # G. C. Greubel, Mar 25 2024