A057868 Denominator of "modified Bernoulli number" b(2n) = Bernoulli(2*n)/(4*n*(2*n)!).

48, 5760, 362880, 19353600, 958003200, 31384184832000, 2092278988800, 341459930972160000, 183927391818153984000, 32114306507931648000000, 620448401733239439360000, 81303558563123696133734400000, 9678995067038535254016000000, 2122022878497528469090467840000000

Offset

1,1

Comments

Note that Weisstein gives the formula b(n) = B(n)/(2*n*n!), and a(n) is the denominator of b(2*n). Numerators seem to be A141590 (not A001067 or A046968 or A255505). - Andrey Zabolotskiy, Dec 03 2022

Links

Table of n, a(n) for n=1..14.

D. Bar-Natan, T. T. Q. Le and D. P. Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geometry and Topology 7-1 (2003) 1-31.

Eric Weisstein's World of Mathematics, Modified Bernoulli Numbers.

Index entries for sequences related to Bernoulli numbers.

Example

The sequence of modified Bernoulli numbers begins 1/48, -1/5760, 1/362880, -1/19353600, 1/958003200, -691/31384184832000, ...

Maple

seq(denom(bernoulli(2*n)/((4*n)*(2*n)!)), n = 1..14); # Peter Luschny, Dec 03 2022

Mathematica

a[n_] := Denominator[ BernoulliB[2n] / (8n^2*(2n-1)!)];
Table[a[n], {n, 1, 12}] (* Jean-François Alcover, Jun 07 2012 *)

Crossrefs

Numerators seem to be A141590.

Cf. A001067.

Sequence in context: A222846 A265666 A114721 * A269179 A276098 A233242

Adjacent sequences: A057865 A057866 A057867 * A057869 A057870 A057871

Keyword

nonn,frac

Author

Eric W. Weisstein

Extensions

Name edited by Andrey Zabolotskiy, Dec 03 2022

Status

approved