A100652 Denominator of 1 - Sum_{i=1..n} |Bernoulli(i)|.

1, 2, 3, 3, 10, 10, 105, 105, 70, 70, 1155, 1155, 1430, 1430, 2145, 2145, 24310, 24310, 4849845, 4849845, 58786, 58786, 2028117, 2028117, 965770, 965770, 1448655, 1448655, 28007330, 28007330, 100280245065, 100280245065, 66853496710, 66853496710, 100280245065

Offset

1,2

Comments

Contribution from Paul Curtz, Aug 07 2012 (Start):

Take a(0)=1. Then instead of the Akiyama-Tanigawa algorithm we create the extended (or prolonged) Akiyama-Tanigawa algorithm using A028310(n)=1,1,2,3,4,5,... instead of A000027(n)=1,2,3,4,5,.. .

Hence the array (A051714 with an additional column)

2, 1, 1/2, 1/3, 1/4,

1, 1/2, 1/3, 1/4, 1/5,

1/2, 1/6, 1/6, 3/20, 2/15, A026741(n+1)/A045896(n+1)

1/3, 0, 1/30, 1/20, 2/35, A194531(n)/A193220(n)

1/3, -1/30, -1/30, -3/140, -1/105. A051722(n)/A051723(n).

a(n) is the denominator of the (first) column before the Akiyama-Tanigawa algorithm leading to the second Bernoulli numbers A164555(n)/A027642(n). See A176672(n).

(End)

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

1, 1/2, 1/3, 1/3, 3/10, 3/10, 29/105, 29/105, 17/70, 17/70, 193/1155, 193/1155, -123/1430, -123/1430, -2687/2145, -2687/2145, -202863/24310, -202863/24310, -307072861/4849845, ... = A100651/A100652.

Mathematica

Denominator[1-(Accumulate[Abs[BernoulliB[Range[0, 40]]]])] (* Harvey P. Dale, Jan 28 2013 *)

Crossrefs

Sequence in context: A364967 A337432 A123027 * A094416 A218868 A329874

Adjacent sequences: A100649 A100650 A100651 * A100653 A100654 A100655

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 05 2004

Status

approved