A270707 a(n) = (n+1)!*Sum_{k=0..(n-1)/2}(k!*stirling1(n-k,k+1)*(-1)^(n+1)/(n-k)!/(k+1)!).

0, 2, 3, 14, 60, 349, 2310, 17772, 154224, 1494168, 15973980, 186815386, 2372249880, 32503673760, 477955820160, 7507517217600, 125452772867520, 2222130456911520, 41587962405967872, 820019478835203840, 16990772582549183040

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: A268559 A346057 A371608 * A141148 A275554 A346553

Adjacent sequences: A270704 A270705 A270706 * A270708 A270709 A270710

Keyword

nonn

Author

Vladimir Kruchinin, Mar 22 2016

Status

approved