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A157809 Numerator of Bernoulli(n,3). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.