OFFSET
0,5
COMMENTS
Reduced a(n)/c(n) = 0, 0, 1, 1/2, 5/3, 13/6, 19/5, 179/30, 1028/105, 1103/70, 893/35, 2889/70, 15445/231, 249787/2310,... .
After the first Bernoulli numbers we consider the same transform applied to the second Bernoulli numbers A164555(n)/A027642(n). Hence reduced b(n)/c(n) = 0, 0, 1, 3/2, 8/3, 25/6, 34/5, 329/30, 1868/105, 2013/70, 1628/35, 5269/70, 28150/231, 455377/2310, ....
Conjecture: (b(n)-a(n))/c(n) = 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ..., that is two 0 followed by A000045.
This conjecture is confirmed up to 100 terms. [Jean-François Alcover, Jul 19 2013]
EXAMPLE
MATHEMATICA
b1[0] = b1[1] = 0; b1[n_] := b1[n] = b1[n - 1] + b1[n - 2] + BernoulliB[n - 2]; a[n_] := Numerator[b1[n]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 19 2013 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Paul Curtz, Jul 13 2013
EXTENSIONS
More terms from Jean-François Alcover, Jul 19 2013
STATUS
approved