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Denominator of b_{2n}(1/4), where b_{n}(x) are Nörlund's generalized Bernoulli polynomials.
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%I #12 Jun 28 2019 07:14:55

%S 1,24,320,10752,184320,360448,23855104,94371840,285212672,

%T 267764367360,3720515420160,987842478080,201004469452800,

%U 103903848824832,637716744110080,11997870882291712,368450744514248704,2251799813685248,164633587978155851776,9367487224930631680

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

%C See A239792 for references.

%F 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)).

%p b := proc(n) option remember; if n < 1 then 1 else

%p -add(binomial(n-1, k-1)*bernoulli(k)*b(n-k)/k, k= 2..n)/2 fi end:

%p A239793 := n -> denom(b(2*n));

%p seq(A239793(n), n=0..19);

%t b[n_] := b[n] = If[n < 1, 1, -Sum[Binomial[n - 1, k - 1] BernoulliB[k] b[n - k]/k, {k, 2, n}]/2];

%t a[n_] := b[2 n] // Denominator;

%t Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Jun 28 2019 *)

%Y Cf. A220412, A239792 (numerators).

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Mar 26 2014