|
|
A238163
|
|
a(n) is the nearest integer to 8*(2*n+1)! * Bernoulli(2*n,1/2).
|
|
2
|
|
|
8, -4, 28, -930, 96012, -24144750, 12602990070, -12203470904625, 20180112406353900, -53495387545025175750, 216267236072968468547250, -1280630367874799320798794375, 10743714652441927865738713818750, -124178158916511109662405449217796875
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
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
|
|
|
MATHEMATICA
|
a[n_] := Round[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* Robert G. Wilson v, Feb 17 2014 *)
|
|
PROG
|
(PARI) A238163=n->round(8*(2*n+1)!*subst(bernpol(2*n, x), x, 1/2)) \\ M. F. Hasler, Feb 16 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|