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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
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.
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