A157809 Numerator of Bernoulli(n,3).

1, 5, 37, 15, 1079, 85, 8317, 455, 30959, 2313, 338585, 11275, 67124549, 53261, 688219, 245775, 267391423, 1114129, 1882776439, 4980755, 3460132789, 22020117, 6367811021, 96469015, 549385297589, 419430425, 5243044651, 1811939355, 3245794417411, 7784628253

Offset: 0

Author

N. J. A. Sloane, Nov 10 2009

Keywords

• sign
• frac

Comments

From Paul Curtz, Feb 18 2015 (Start)

The fractions 1, 5/2, 37/6, 15, 1079/30, 85, 8317/42, 455, 30959/30 etc are the binomial transform of the sequence of fractions Bernoulli(n,2) = 1, 3/2, 13/6, 3, 119/30, 5, 253/42 specified in A164558.

Their table of repeated differences starts

1, 5/2, 37/6, 15, 1079/30, ...

3/2, 11/3, 53/6, 629/30, ...

13/6, 31/6, 182/15, ...

3, 209/30, ...

119/30, ...

etc.

The sums of the antidiagonals in this table of differences are n*2^(n-1)

1 = 1

3/2 + 5/2 = 4

13/6 + 11/3 + 37/6 = 12

3 + 31/6 + 53/6 + 15 = 32

etc, see A001787.

(End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..250

Crossrefs

For denominators see A027642.

Programs

Maple

seq(numer(bernoulli(n,3)),n=0..50); # Robert Israel, Jul 03 2016

Mathematica

Table[Numerator[BernoulliB[n, 3]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)