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Numerators from expansion of e.g.f. (x^3/3!)/(e^x-1-x-(x^2/2!)).
1

%I #35 Mar 01 2020 04:49:30

%S 1,-1,1,1,1,-1,-13,7,7453,6669,-114753,-123387,-7307779,4681807,

%T 37377631,3949479,-309016992029,-139291594927,1061523546157,

%U 562200661481,12828113969679941,-446763044161503,-17777677128737999,-3490123799181493,7248496389957890833,196409682891987107

%N Numerators from expansion of e.g.f. (x^3/3!)/(e^x-1-x-(x^2/2!)).

%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 Numerator[(#! SeriesCoefficient[(x^3/6)/(E^x - 1 - x - x^2/2), {x, 0, #}] & /@ Range[0, 25])]

%o (Sage)

%o def A249024_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).numerator())

%o return R

%o print(A249024_list(26)) # _Peter Luschny_, Feb 20 2016

%Y Cf. A248964 (denominators).

%K sign,frac

%O 0,7

%A _Christopher Ernst_, Oct 19 2014