

A238163


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
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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 R. 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^log2(n+1). This yields A238164 as an alternative way of producing an integer sequence based on (2n+1)! B[2n](1/2).


LINKS

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


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

Cf. A033473, A238015, A238164.
Sequence in context: A160415 A160411 A033473 * A213773 A213178 A082682
Adjacent sequences: A238160 A238161 A238162 * A238164 A238165 A238166


KEYWORD

sign


AUTHOR

M. F. Hasler, Feb 18 2014


STATUS

approved



