A075178 Denominators of expansion of 1/x+1/log(1-x).

2, 12, 12, 120, 20, 504, 168, 720, 180, 1320, 88, 65520, 10920, 5040, 720, 24480, 68, 28728, 3192, 39600, 27720, 182160, 1840, 1965600, 163800, 39312, 3024, 97440, 2320, 3437280, 229152, 3769920, 235620, 42840, 280, 138181680, 219336, 35568, 1872, 3247200

Offset

0,1

Comments

The numerator sequence is |A006232(n+1)|, n>=0.

|A006232(n+1)|= numerator(r(n)), n>=1, with r(n) := sum(|stirling1(n,k)|*B(k+1)/(k+1),k=1..n), n>=1 and B(n): =A027641(n)/A027642(n) (Bernoulli numbers) and stirling1(n,m)=A008275(n,m), n>=m>=1; r(0) := 1/2.

Links

Table of n, a(n) for n=0..39.

Formula

Denominators from e.g.f. 1/x + 1/log(1-x) (and of signed sequence from e.g.f. 1/x - 1/log(1+x)).

a(n) = denominator(r(n)), n>=0, with rational r(n) defined in one of the comments.

Example

r(n) sequence, n>=0: 1/2, 1/12, 1/12, 19/120, 9/20, 863/504, 1375/168, 33953/720, 57281/180,...

Mathematica

With[{nn=40}, Denominator[CoefficientList[Series[1/x+1/Log[1-x], {x, 0, nn}] , x] Range[0, nn]!]] (* Harvey P. Dale, Feb 18 2012 *)

Prog

(Sage)
def A075178_list(len):
    f, R, C = 1, [0], [1]+[0]*len
    for n in (1..len):
        for k in range(n, 0, -1):
            C[k] = -C[k-1] * k / (k + 1)
        C[0] = -sum(C[k] for k in (1..n))
        R.append((C[0]*f).denominator())
        f *= n
    return R[1:]
print(A075178_list(40)) # Peter Luschny, Feb 21 2016

Crossrefs

Cf. A006232, A075179, A006232 with A006233, A008275.

Sequence in context: A371375 A198532 A198477 * A145618 A306693 A169900

Adjacent sequences: A075175 A075176 A075177 * A075179 A075180 A075181

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Sep 06, 2002

Status

approved