A213448 - OEIS

%I N2000 #16 Jan 24 2020 10:22:32

%S 1,9,1375,114562,9458775,24466579093,1681457720761,18293695492500,

%T 168930583738812489,161867055619224199787,48189699568363802160789,

%U 192060902780872132330221667,26975418307200573459970703125,7644290462843582490448119097743

%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.

%p A213448 := proc(n)

%p         local nu ;

%p         nu := 2*n+3 ;

%p         mul(t-i,i=0..nu-1) ;

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

%p         abs(numer( %)) ;

%p end proc:

%p seq(A213448(n),n=0..15) ; # _R. J. Mathar_, Jun 26 2012

%t a[n_] := With[{nu = 2n+3}, Integrate[Product[t-i, {i, 0, nu-1}], {t, 0, 1}]*(nu-1) // Numerator // Abs];

%t a /@ Range[0, 13] (* _Jean-François Alcover_, Jan 24 2020, after _R. J. Mathar_ *)

%K nonn,frac

%O 0,2

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