A213447 Numerators of higher order Bernoulli numbers. (Formerly N1999)

1, 9, 475, 36799, 2082753, 262747265, 1382741929621, 5362709743125, 15980174332775873, 24919383499187492303, 5370601980438646999929, 4365522871220234892455639, 23440607720186374192676171875, 277027686598268613994459361577

Offset

0,2

Comments

See Nørlund for precise definition.

References

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

Links

Table of n, a(n) for n=0..13.

N. E. Nørlund, Vorlesungen über Differenzenrechnung, Springer, 1924, p. 461 and p. 147.

Maple

A213447 := proc(n)
        local nu ;
        nu := 2*n+1 ;
        mul(t-i, i=1..nu) ;
        int(%, t=0..1) ;
        abs(numer( %)) ;
end proc:
seq(A213447(n), n=0..15) ; # R. J. Mathar, Jun 26 2012

Mathematica

a[n_] := Integrate[Product[t-i, {i, 1, 2n+1}], {t, 0, 1}] // Numerator // Abs;
a /@ Range[0, 13] (* Jean-François Alcover, Apr 04 2020 *)

Crossrefs

Sequence in context: A061175 A289054 A166879 * A128947 A293951 A267236

Adjacent sequences: A213444 A213445 A213446 * A213448 A213449 A213450

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 12 2012

Status

approved