A238163 a(n) is the nearest integer to 8*(2*n+1)! * Bernoulli(2*n,1/2).

8, -4, 28, -930, 96012, -24144750, 12602990070, -12203470904625, 20180112406353900, -53495387545025175750, 216267236072968468547250, -1280630367874799320798794375, 10743714652441927865738713818750, -124178158916511109662405449217796875

Offset: 0

Author

M. F. Hasler, Feb 18 2014

Keywords

• sign

Comments

See A033473 for the numerators and A238015 for the denominators of 8*(2*n+1)!*Bernoulli(2*n,1/2).

As Robert Israel remarks, this expression is no longer an integer for n = 15, 23, 27, 29, 30, 31, 39, 43, 45, 46, 47, ... That's why "nearest integer" has been prefixed. - M. F. Hasler, Feb 16 2014

It can be seen that the denominator of (2*n+1)! * Bernoulli(2*n,1/2) is never more than 2^log_2(n+1). This yields A238164 as an alternative way of producing an integer sequence based on (2n+1)! * Bernoulli(2*n,1/2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Cf. A033473, A238015, A238164.

Programs

Mathematica

a[n_] := Round[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* Robert G. Wilson v, Feb 17 2014 *)

PARI

A238163=n->round(8*(2*n+1)!*subst(bernpol(2*n,x),x,1/2)) \\ M. F. Hasler, Feb 16 2014