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Denominator of "modified Bernoulli number" b(2n) = Bernoulli(2*n)/(4*n*(2*n)!).
1

%I #29 Dec 03 2022 16:31:17

%S 48,5760,362880,19353600,958003200,31384184832000,2092278988800,

%T 341459930972160000,183927391818153984000,32114306507931648000000,

%U 620448401733239439360000,81303558563123696133734400000,9678995067038535254016000000,2122022878497528469090467840000000

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

%C 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

%H D. Bar-Natan, T. T. Q. Le and D. P. Thurston, <a href="https://arxiv.org/abs/math/0204311">Two applications of elementary knot theory to Lie algebras and Vassiliev invariants</a>, Geometry and Topology 7-1 (2003) 1-31.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModifiedBernoulliNumber.html">Modified Bernoulli Numbers</a>.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.

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

%p seq(denom(bernoulli(2*n)/((4*n)*(2*n)!)), n = 1..14); # _Peter Luschny_, Dec 03 2022

%t a[n_] := Denominator[ BernoulliB[2n] / (8n^2*(2n-1)!)];

%t Table[a[n], {n, 1, 12}] (* _Jean-François Alcover_, Jun 07 2012 *)

%Y Numerators seem to be A141590.

%Y Cf. A001067.

%K nonn,frac

%O 1,1

%A _Eric W. Weisstein_

%E Name edited by _Andrey Zabolotskiy_, Dec 03 2022