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

Author

Peter Luschny, Mar 26 2014

Keywords

• nonn
• frac

Comments

See A239792 for references.

Crossrefs

Cf. A220412, A239792 (numerators).

Programs

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 *)

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)).