A157809 - OEIS

%I #15 Jul 04 2016 03:55:55

%S 1,5,37,15,1079,85,8317,455,30959,2313,338585,11275,67124549,53261,

%T 688219,245775,267391423,1114129,1882776439,4980755,3460132789,

%U 22020117,6367811021,96469015,549385297589,419430425,5243044651,1811939355,3245794417411,7784628253

%N Numerator of Bernoulli(n,3).

%C From _Paul Curtz_, Feb 18 2015 (Start)

%C 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 Their table of repeated differences starts

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

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

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

%C 3,      209/30, ...

%C 119/30, ...

%C etc.

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

%C 1                       =  1

%C 3/2  +  5/2             =  4

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

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

%C etc, see A001787.

%C (End)

%H Vincenzo Librandi, <a href="/A157809/b157809.txt">Table of n, a(n) for n = 0..250</a>

%p seq(numer(bernoulli(n,3)),n=0..50); # _Robert Israel_, Jul 03 2016

%t Table[Numerator[BernoulliB[n, 3]], {n, 0, 50}] (* _Vincenzo Librandi_, Mar 16 2014 *)

%Y For denominators see A027642.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 10 2009