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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
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
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
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 10 2009
STATUS
approved