Voozh

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..625

OEIS Wiki, Autosequence.

EXAMPLE

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, ...

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 *)

PROG

(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