OFFSET
0,3
COMMENTS
Difference table of 1, 1, 1/6, 0, -1/30, ... :
1, 1, 1/6, 0, -1/30, 0, 1/42, 0, ...
0, -5/6, -1/6, -1/30, 1/30, 1/42, -1/42, ...
-5/6, 2/3, 2/15, 1/15, -1/105, -1/21, ...
3/2, -8/15, -1/15, -8/105, -4/105, ...
-61/30, 7/15, -1/105, 4/105, ...
5/2, -10/21, 1/21, ...
-125/42, 11/21, ...
7/2, ...
etc.
The inverse binomial transform is the first column. a(n) is the n-th term of the numerators. See A027641(n+1).
Denominators: A176591.
Is a(4n+2) a multiple of 5? This is true, at least up to 4n+2 = 998. - Jean-François Alcover, Jul 02 2015
LINKS
Colin Barker, Table of n, a(n) for n = 0..629
FORMULA
EXAMPLE
By the first formula: numerators of 1-0=1, -1/2+1/2=0, 1/6-1=-5/6, 0+3/2=3/2,....
MATHEMATICA
max = 40; B[1] = 1; B[n_] := BernoulliB[n]; BB = Array[B, max, 0]; a[n_] := Differences[BB, n] // First // Numerator; Table[a[n], {n, 0, max-1}] (* Jean-François Alcover, May 20 2015 *)
PROG
(PARI)
firstdiff(s) = my(t=vector(#s-1)); for(i=2, #s, t[i-1]=s[i]-s[i-1]); t
a257935(k) = {
my(s=[], b = concat([1, 1], vector(k, n, n++; bernfrac(n))));
until(#b<2,
s = concat(s, numerator(b[1]));
b = firstdiff(b)
);
s
}
a257935(50) \\ Colin Barker, May 13 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, May 13 2015
EXTENSIONS
More terms from Colin Barker, May 13 2015
STATUS
approved