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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 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.)