A213450 Numerators of higher order Bernoulli numbers. (Formerly N2200)

1, 19, 4315, 237671, 9751299, 150653570023, 1719676921651, 111956703448001, 515820397142126323, 234948724145929620551, 146676714003698721466337, 2335491919795216159716047077, 27307173331136364105327316225, 15462805586388260782721906167299

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.

Maple

A213450 := proc(n)
        local nu ;
        nu := 2*n+2 ;
        mul(t-i, i=0..nu-1) ;
        int(%, t=0..1)*(nu-1) ;
        abs(numer( %)) ;
end proc:
seq(A213450(n), n=0..15) ; # R. J. Mathar, Jun 26 2012

Mathematica

a[n_] := With[{nu = 2n+2}, Integrate[Product[t-i, {i, 0, nu-1}], {t, 0, 1}]*(nu-1) // Numerator // Abs];
a /@ Range[0, 13] (* Jean-François Alcover, Jan 24 2020, after R. J. Mathar *)

Crossrefs

Sequence in context: A125197 A238563 A281820 * A099809 A271588 A233464

Adjacent sequences: A213447 A213448 A213449 * A213451 A213452 A213453

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 12 2012

Status

approved