A239793 Denominator of b_{2n}(1/4), where b_{n}(x) are Nörlund's generalized Bernoulli polynomials.

1, 24, 320, 10752, 184320, 360448, 23855104, 94371840, 285212672, 267764367360, 3720515420160, 987842478080, 201004469452800, 103903848824832, 637716744110080, 11997870882291712, 368450744514248704, 2251799813685248, 164633587978155851776, 9367487224930631680

Offset

0,2

Comments

See A239792 for references.

Links

Table of n, a(n) for n=0..19.

Formula

Let b(n) = -sum_{2<=k<=n}(C(n-1, k-1)*Bernoulli(k)*b(n-k)/k)/2 for n>0 and otherwise 1. Then a(n) = denominator(b(2*n)).

Maple

b := proc(n) option remember; if n < 1 then 1 else
-add(binomial(n-1, k-1)*bernoulli(k)*b(n-k)/k, k= 2..n)/2 fi end:
A239793 := n -> denom(b(2*n));
seq(A239793(n), n=0..19);

Mathematica

b[n_] := b[n] = If[n < 1, 1, -Sum[Binomial[n - 1, k - 1] BernoulliB[k] b[n - k]/k, {k, 2, n}]/2];
a[n_] := b[2 n] // Denominator;
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Jun 28 2019 *)

Crossrefs

Cf. A220412, A239792 (numerators).

Sequence in context: A069779 A288507 A199301 * A289706 A300846 A006922

Adjacent sequences: A239790 A239791 A239792 * A239794 A239795 A239796

Keyword

nonn,frac

Author

Peter Luschny, Mar 26 2014

Status

approved