A213448 Numerators of higher order Bernoulli numbers. (Formerly N2000)

1, 9, 1375, 114562, 9458775, 24466579093, 1681457720761, 18293695492500, 168930583738812489, 161867055619224199787, 48189699568363802160789, 192060902780872132330221667, 26975418307200573459970703125, 7644290462843582490448119097743

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

A213448 := proc(n)
        local nu ;
        nu := 2*n+3 ;
        mul(t-i, i=0..nu-1) ;
        int(%, t=0..1)*(nu-1) ;
        abs(numer( %)) ;
end proc:
seq(A213448(n), n=0..15) ; # R. J. Mathar, Jun 26 2012

Mathematica

a[n_] := With[{nu = 2n+3}, 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: A076704 A117053 A270067 * A120347 A230172 A231191

Adjacent sequences: A213445 A213446 A213447 * A213449 A213450 A213451

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 12 2012

Status

approved