|
|
A165161
|
|
Numerator of the n-th term in the first differences of the binomial transform of the "original" Bernoulli numbers.
|
|
2
|
|
|
1, 2, 5, 29, 31, 43, 41, 29, 31, 71, 61, 2039, 3421, 13, -1, -3107, 4127, 44665, -43069, -174281, 174941, 854651, -854375, -236361361, 236366821, 8553109, -8553097, -23749460159, 23749461899, 8615841290327
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The binomial transform of the "original" Bernoulli numbers is 1, 3/2, 13/6, ... as mentioned in A164558.
The first differences of that sequence are 3/2 - 1 = 1/2, 13/6 - 3/2 = 2/3, 5/6, 29/30, 31/30, ... and the numerators of these differences are listed here.
The bisection a(2n) reappears (up to signs) as A162173(n+1).
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
read("transforms") :
A164555 := proc(n) if n <= 2 then 1; else numer(bernoulli(n)) ; end if; end proc:
A027642 := proc(n) denom(bernoulli(n)) ; end proc:
nmax := 40:
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|