A033473 -id:A033473 - cp's OEIS frontend

A238015 Denominator of (2n+1)!8Bernoulli(2n,1/2).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 4, 1, 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 4, 1, 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 1, 1, 2, 1

Offset: 0

Robert Israel, Feb 17 2014

It appears that a(n) is 1 for n in A095736, 2 for n in A014312, 4 for n in A014313, 8 for n in A023688, 16 for n in A023689, 32 for n in A023690, 64 for n in A023691. - Michel Marcus, Feb 18 2014

			For n=15, (2*15+1)!*8*Bernoulli(2*15,1/2) = -79147239268966167007717425917182573906640625/2 so a(15) = 2.

Robert Israel, Table of n, a(n) for n = 0..2000

Cf. A033473.

seq(denom((2*n+1)!*8*bernoulli(2*n,1/2)), n=0 .. 100);

Table[Denominator[(2 n + 1)! 8 BernoulliB[2 n, 1/2]], {n, 0, 200}] (* Vincenzo Librandi, Feb 18 2014 *)

A238164 2^floor(log[2](n+1))(2n+1)!Bernoulli(2n,1/2).

Original entry on oeis.org

1, -1, 7, -465, 48006, -12072375, 6301495035, -12203470904625, 20180112406353900, -53495387545025175750, 216267236072968468547250, -1280630367874799320798794375, 10743714652441927865738713818750, -124178158916511109662405449217796875, 1930915681227482441797773554892002071875

Offset: 0

M. F. Hasler, Feb 18 2014

sign

Motivated by the original definition of A033473 which turned out to produce a non-integer sequence.

M. F. Hasler, Table of n, a(n) for n = 0..50
Index entries for sequences related to Bernoulli numbers.

n->(2*n+1)!*subst(bernpol(2*n,x),x,1/2)<<(log(n+1)\log(2))

A238163 a(n) is the nearest integer to 8(2n+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

M. F. Hasler, Feb 18 2014

sign

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).

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

Cf. A033473, A238015, A238164.

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

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

cp's OEIS Frontend

A238015 Denominator of (2n+1)!8Bernoulli(2n,1/2).

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A238164 2^floor(log[2](n+1))(2n+1)!Bernoulli(2n,1/2).

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

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cp's OEIS Frontend

A238015 Denominator of (2*n+1)!*8*Bernoulli(2*n,1/2).

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Maple

Mathematica

A238164 2^floor(log[2](n+1))*(2*n+1)!*Bernoulli(2*n,1/2).

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PARI

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

Views

Author

Keywords

Comments

Links

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Programs

Mathematica

PARI

A238015 Denominator of (2n+1)!8Bernoulli(2n,1/2).

A238164 2^floor(log[2](n+1))(2n+1)!Bernoulli(2n,1/2).

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