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

0,2

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

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 *)

Crossrefs

For denominators see A027642.

Sequence in context: A222592 A174507 A119483 * A079339 A257343 A244927

Adjacent sequences: A157806 A157807 A157808 * A157810 A157811 A157812

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 10 2009

Status

approved