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 A270707 a(n) = (n+1)!*Sum_{k=0..(n-1)/2}(k!*stirling1(n-k,k+1)*(-1)^(n+1)/(n-k)!/(k+1)!). 1
 0, 2, 3, 14, 60, 349, 2310, 17772, 154224, 1494168, 15973980, 186815386, 2372249880, 32503673760, 477955820160, 7507517217600, 125452772867520, 2222130456911520, 41587962405967872, 820019478835203840, 16990772582549183040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 FORMULA E.g.f.: (log(1/(1-x))+x/(1-x))*(1/(1-x)^x-1)/(x*log(1/(1-x))). a(n) ~ n! * n/log(n) * (1 + (1-gamma)/log(n) + (gamma^2 - 2*gamma + 2 - Pi^2/6)/log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 22 2016 MATHEMATICA Table[(n+1)!*Sum[k!*StirlingS1[n-k, k+1]*(-1)^(n+1)/(n-k)!/(k+1)!, {k, 0, (n-1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 22 2016 *) PROG (Maxima) makelist((n)!*coeff(taylor((log(1/(1-x))+x/(1-x))*(1/(1-x)^x-1)/(x*log(1/(1-x))), x, 0, 15), x, n), n, 0, 15); a(n):=(n+1)!*sum((k)!*stirling1(n-k, k+1)*(-1)^(n+1)/(n-k)!/(k+1)!, k, 0, (n-1)/2); (PARI) for(n=0, 20, print1((n+1)!*sum(k=0, (n-1)/2,  k!*stirling(n-k, k+1, 1)*(-1)^(n+1)/(n-k)!/(k+1)!), ", ")) \\ G. C. Greubel, Sep 07 2018 CROSSREFS Cf. A048994. Sequence in context: A153741 A070207 A268559 * A141148 A275554 A064184 Adjacent sequences:  A270704 A270705 A270706 * A270708 A270709 A270710 KEYWORD nonn AUTHOR Vladimir Kruchinin, Mar 22 2016 STATUS approved

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Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)