A248964 Denominators from expansion of e.g.f. (x^3/3!)/(e^x-1-x-(x^2/2!)).

1, 4, 40, 160, 5600, 896, 19200, 76800, 14784000, 19712000, 512512000, 186368000, 19568640000, 6021120000, 20889600000, 7798784000, 71310131200000, 16778854400000, 503365632000000, 15138816000000, 221798793216000000, 6035341312000000

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Daniel Berhanu, Hunduma Legesse, Arithmetical properties of hypergeometric bernoulli numbers, Indagationes Mathematicae, 2016.

Formula

E.g.f: (x^3/3!)/(e^x - 1 - x - (x^2/2!)).

Example

E.g.f. coefficients are 1, -1/4, 1/40, 1/160, 1/5600, -1/896, -13/19200, 7/76800, ...

Mathematica

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

Prog

(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
(Sage)
def A248964_list(len):
    f, R, C = 1, [1], [1]+[0]*(len-1)
    for n in (1..len-1):
        f *= n
        for k in range(n, 0, -1):
            C[k] = C[k-1] / (k+3)
        C[0] = -sum(C[k] for k in (1..n))
        R.append((C[0]*f).denominator())
    return R
print(A248964_list(22)) # Peter Luschny, Feb 20 2016

Crossrefs

Cf. A249024 (numerators).

Sequence in context: A355841 A187378 A199833 * A224086 A271013 A163322

Adjacent sequences: A248961 A248962 A248963 * A248965 A248966 A248967

Keyword

nonn,frac

Author

Christopher Ernst, Oct 18 2014

Status

approved