login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229979 Numerators of interleaved A063524(n) and A002427(n)/A006955(n). 3
0, 1, 1, 1, 0, -1, 0, 1, 0, -3, 0, 5, 0, -691, 0, 35, 0, -3617, 0, 43867, 0, -1222277, 0, 854513, 0, -1181820455, 0, 76977927, 0, -23749461029, 0, 8615841276005, 0, -84802531453387, 0, 90219075042845, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
COMMENTS
Numerators of Br(n) = 0, 1, 1, 1/2, 0, -1/6, 0, 1/6, 0, -3/10, 0, 5/6, 0, -691/210,... complementary Bernoulli numbers.
A164555(n)/A027642(n) is an autosequence of second kind. Its inverse binomial transform is the signed sequence and its main diagonal is the double of the first upper diagonal.
Br(n) is an autosequence of first kind. Its inverse binomial transform is the signed sequence and its main diagonal is A000004=0's.
Br(n) difference table:
0, 1, 1, 1/2, 0, -1/6,...
1, 0, -1/2, -1/2, -1/6, 1/6,... =A140351(n)/A140219(n)
-1, -1/2, 0, 1/3, 1/3, 0,...
1/2, 1/2, 1/3, 0, -1/3, -1/3,...
0, -1/6, -1/3, -1/3, 0, 8/15,...
-1/6, -1/6, 0, 1/3, 8/15, 0,... etc.
LINKS
FORMULA
a(2n)=A063524(n). a(2n+1)=A002427(n).
a(n) = numerators of n * b(n) with b(n)=0 followed by A164555(n)/A027642(n) = 0, 1, 1/2, 1/6, 0,... in A165142(n).
a(n+1) = numerators of Br(n+1) = Br(n) + A140351(n)/A140219(n), a(0)=Br(0)=0.
MATHEMATICA
a[0] = 0; a[1] = a[2] = 1; a[n_] := 2*n*BernoulliB[n-1] // Numerator; Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Nov 25 2013 *)
CROSSREFS
Cf. A050925: a similar sequence, because 2*(n+1)*B(n) and (n+1)*B(n) have the same numerator.
Sequence in context: A047760 A276908 A242246 * A050925 A086696 A259743
KEYWORD
sign,frac
AUTHOR
Paul Curtz, Oct 05 2013
EXTENSIONS
Cross-ref. to A050925 by Jean-François Alcover, Dec 09 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)