A213447 - OEIS

%I N1999 #17 Apr 04 2020 10:30:44

%S 1,9,475,36799,2082753,262747265,1382741929621,5362709743125,

%T 15980174332775873,24919383499187492303,5370601980438646999929,

%U 4365522871220234892455639,23440607720186374192676171875,277027686598268613994459361577

%N Numerators of higher order Bernoulli numbers.

%C See Nørlund for precise definition.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%H N. E. Nørlund, <a href="http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN373206070">Vorlesungen über Differenzenrechnung</a>, Springer, 1924, p. 461 and p. 147.

%p A213447 := proc(n)

%p         local nu ;

%p         nu := 2*n+1 ;

%p         mul(t-i,i=1..nu) ;

%p         int(%,t=0..1) ;

%p         abs(numer( %)) ;

%p end proc:

%p seq(A213447(n),n=0..15) ; # _R. J. Mathar_, Jun 26 2012

%t a[n_] := Integrate[Product[t-i, {i, 1, 2n+1}], {t, 0, 1}] // Numerator // Abs;

%t a /@ Range[0, 13] (* _Jean-François Alcover_, Apr 04 2020 *)

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Jun 12 2012