cp's OEIS Frontend

A157809 Numerator of Bernoulli(n,3).

%I A157809 #15 Jul 04 2016 03:55:55
%S A157809 1,5,37,15,1079,85,8317,455,30959,2313,338585,11275,67124549,53261,
%T A157809 688219,245775,267391423,1114129,1882776439,4980755,3460132789,
%U A157809 22020117,6367811021,96469015,549385297589,419430425,5243044651,1811939355,3245794417411,7784628253
%N A157809 Numerator of Bernoulli(n,3).
%C A157809 From _Paul Curtz_, Feb 18 2015 (Start)
%C A157809 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.
%C A157809 Their table of repeated differences starts
%C A157809 1,         5/2,   37/6,     15, 1079/30, ...
%C A157809 3/2,      11/3,   53/6, 629/30, ...
%C A157809 13/6,     31/6, 182/15, ...
%C A157809 3,      209/30, ...
%C A157809 119/30, ...
%C A157809 etc.
%C A157809 The sums of the antidiagonals in this table of differences are n*2^(n-1)
%C A157809 1                       =  1
%C A157809 3/2  +  5/2             =  4
%C A157809 13/6 + 11/3 + 37/6      = 12
%C A157809 3    + 31/6 + 53/6 + 15 = 32
%C A157809 etc, see A001787.
%C A157809 (End)
%H A157809 Vincenzo Librandi, <a href="/A157809/b157809.txt">Table of n, a(n) for n = 0..250</a>
%p A157809 seq(numer(bernoulli(n,3)),n=0..50); # _Robert Israel_, Jul 03 2016
%t A157809 Table[Numerator[BernoulliB[n, 3]], {n, 0, 50}] (* _Vincenzo Librandi_, Mar 16 2014 *)
%Y A157809 For denominators see A027642.
%K A157809 sign,frac
%O A157809 0,2
%A A157809 _N. J. A. Sloane_, Nov 10 2009