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A075178 Denominators of expansion of 1/x+1/log(1-x). 5
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 (list; graph; refs; listen; history; text; internal format)
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: A226393 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

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)