A249024 Numerators from expansion of e.g.f. (x^3/3!)/(e^x-1-x-(x^2/2!)).

1, -1, 1, 1, 1, -1, -13, 7, 7453, 6669, -114753, -123387, -7307779, 4681807, 37377631, 3949479, -309016992029, -139291594927, 1061523546157, 562200661481, 12828113969679941, -446763044161503, -17777677128737999, -3490123799181493, 7248496389957890833, 196409682891987107

Offset

0,7

Links

Table of n, a(n) for n=0..25.

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

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

Prog

(Sage)
def A249024_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).numerator())
    return R
print(A249024_list(26)) # Peter Luschny, Feb 20 2016

Crossrefs

Cf. A248964 (denominators).

Sequence in context: A177427 A110056 A159562 * A076116 A010216 A302456

Adjacent sequences: A249021 A249022 A249023 * A249025 A249026 A249027

Keyword

sign,frac

Author

Christopher Ernst, Oct 19 2014

Status

approved