A239792 -id:A239792 - cp's OEIS frontend

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

Peter Luschny, Mar 26 2014

See A239792 for references.

Cf. A220412, A239792 (numerators).

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);

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 *)

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)).

A239795 a(n) = A239793(n)/2^(3*n).

Original entry on oeis.org

1, 3, 5, 21, 45, 11, 91, 45, 17, 1995, 3465, 115, 2925, 189, 145, 341, 1309, 1, 9139, 65, 2255, 148995, 108675, 1645, 270725, 21879, 583, 4389, 4959, 59, 1548729, 27027, 60775, 130985, 15525, 1065, 66047553, 2567565, 39, 2133, 56457, 1411, 8161615, 2639

Offset: 0

Peter Luschny, Mar 26 2014

nonn

See A239792 for references.

Cf. A220412, A239792.

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:
A239795 := n -> denom(b(2*n))/2^(3*n):
seq(A239795(n), n=0..43);

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))/2^(3*n).

cp's OEIS Frontend

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

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