cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A033473 Numerator of (2*n+1)!*8*Bernoulli(2*n,1/2).

Original entry on oeis.org

8, -4, 28, -930, 96012, -24144750, 12602990070, -12203470904625, 20180112406353900, -53495387545025175750, 216267236072968468547250, -1280630367874799320798794375, 10743714652441927865738713818750, -124178158916511109662405449217796875
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

As R. Israel remarks, the expression (2*n+1)!*8*Bernoulli(2*n,1/2) is no longer an integer for n = 15, 23, 27, 29, 30, 31, 39, 43, 45, 46, 47,... - M. F. Hasler, Feb 16 2014
Denominators are in A238015. See A238163 for the rounded values and A238164 for another maybe more interesting variant. - M. F. Hasler, Mar 01 2014

Links

Crossrefs

Cf. A238163, A238164.

Programs

  • Mathematica
    a[n_] := Numerator[ (2 n + 1)! 8 BernoulliB[2 n, 1/2]]; Array[a, 14, 0] (* Robert G. Wilson v, Feb 17 2014, edited by M. F. Hasler, Mar 01 2014 *)
Table[Numerator[(2 n + 1)! 8 BernoulliB[2 n, 1/2]], {n, 0, 20}] (* Vincenzo Librandi, Feb 18 2014 *)
  • PARI
    A033473 = n->numerator((2*n+1)!*8*subst(bernpol(2*n,x),x,1/2)) \\ M. F. Hasler, Feb 16-18 2014

Extensions

Definition changed by M. F. Hasler, Feb 16 2014
Further edits by M. F. Hasler, Mar 01 2014

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

Original entry on oeis.org

8, -4, 28, -930, 96012, -24144750, 12602990070, -12203470904625, 20180112406353900, -53495387545025175750, 216267236072968468547250, -1280630367874799320798794375, 10743714652441927865738713818750, -124178158916511109662405449217796875
Offset: 0

Views

Author

M. F. Hasler, Feb 18 2014

Keywords

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

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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