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The denominators of J. L. Fields generalized Bernoulli polynomials.
3

%I #10 Jun 27 2019 08:38:53

%S 1,-6,60,-504,2160,-3168,786240,-51840,1762560,-82736640,1437004800,

%T -858470400,101896704000,-1881169920,8659353600,-855305256960,

%U 14071151001600,-150493593600,8252165711462400,-70431001804800,24434139856896000,-1076294062964736000

%N The denominators of J. L. Fields generalized Bernoulli polynomials.

%C See A220412 for definitions and references.

%t F[0, _] = 1; F[n_, x_] := F[n, x] = -2x Sum[Binomial[n-1, 2k+1] BernoulliB[2k+2]/(2k+2) F[n-2k-2, x], {k, 0, n/2-1}] // Expand;

%t a[n_] := (-1)^n Denominator[Together[F[2n, x]]];

%t Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Jun 27 2019 *)

%K sign

%O 0,2

%A _Peter Luschny_, Dec 30 2012