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%I #48 Mar 01 2020 04:34:38
%S 1,4,40,160,5600,896,19200,76800,14784000,19712000,512512000,
%T 186368000,19568640000,6021120000,20889600000,7798784000,
%U 71310131200000,16778854400000,503365632000000,15138816000000,221798793216000000,6035341312000000
%N Denominators from expansion of e.g.f. (x^3/3!)/(e^x-1-x-(x^2/2!)).
%H Daniel Berhanu, Hunduma Legesse, <a href="http://dx.doi.org/10.1016/j.indag.2016.11.014">Arithmetical properties of hypergeometric bernoulli numbers</a>, Indagationes Mathematicae, 2016.
%F E.g.f: (x^3/3!)/(e^x - 1 - x - (x^2/2!)).
%e E.g.f. coefficients are 1, -1/4, 1/40, 1/160, 1/5600, -1/896, -13/19200, 7/76800, ...
%t Denominator[(#! SeriesCoefficient[(x^3/6)/( E^x - 1 - x - x^2/2), {x, 0, #}] & /@ Range[0, 25])]
%o (PARI) x = y + O(y^30); v = Vec(serlaplace((x^3/3!)/(exp(x)-1-x-(x^2/2!)))); for (i=1, #v, print1(denominator(v[i]), ", ")); \\ _Michel Marcus_, Oct 18 2014
%o (Sage)
%o def A248964_list(len):
%o f, R, C = 1, [1], [1]+[0]*(len-1)
%o for n in (1..len-1):
%o f *= n
%o for k in range(n, 0, -1):
%o C[k] = C[k-1] / (k+3)
%o C[0] = -sum(C[k] for k in (1..n))
%o R.append((C[0]*f).denominator())
%o return R
%o print(A248964_list(22)) # _Peter Luschny_, Feb 20 2016
%Y Cf. A249024 (numerators).
%K nonn,frac
%O 0,2
%A _Christopher Ernst_, Oct 18 2014
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