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A108125
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Expansion of e.g.f.: x/(1 - log(1+x)).
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3
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0, 1, 2, 3, 8, 20, 84, 266, 1728, 5400, 62400, 105072, 3831552, -6751056, 393519840, -2647115280, 63975266304, -747746339328, 15068270944512, -236303000537472, 4743900735943680, -88955061630656256, 1889497707746457600, -40170338917074339840, 919697318458416414720
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OFFSET
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0,3
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LINKS
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FORMULA
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(n-1) a(n) + (n^2-2n) a(n-1) = Sum_{j=1..n-1} C(n,j) a(j) a(n-j). - Robert Israel, Jul 13 2015
For n > 1, a(n) = n!*Sum_{k=1..n-1} a(n-k)*(-1)^(k+1)/(k*(n-k)!). - Tani Akinari, Nov 25 2017
a(n) ~ n! * (-1)^n / (n * (log(n))^2) * (1 - 2*(gamma + 1) / log(n) + (3*gamma^2 + 6*gamma + 3 - Pi^2/2) / (log(n))^2), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Nov 29 2017
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MAPLE
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G:=x/(1-ln(1+x)): Gser:=series(G, x=0, 28): 0, seq(n!*coeff(Gser, x^n), n=1..25); # yields the signed sequence
A:= proc(n) option remember;
(-(n^2-2*n)*procname(n-1) + add(binomial(n, j)*procname(j)*procname(n-j), j=1..n-1))/(n-1) end proc:
A(0):= 0: A(1):= 1:
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MATHEMATICA
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Range[0, 25]! CoefficientList[Series[x/(1 - Log[1 + x]), {x, 0, 25}], x] (* Vincenzo Librandi, Jul 06 2015 *)
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PROG
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(Maxima)
a[n]:=if n<2 then n else n!*sum(a[n-k]*(-1)^(k+1)/(k*
(n-k)!), k, 1, n-1); makelist(a[n], n, 0, 100); /* Tani Akinari, Nov 25 2017 */
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(x/(1 - log(1+x))))) \\ G. C. Greubel, Aug 30 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(x/(1 - Log(1+x)))); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Aug 30 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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