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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)!). 0
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

Table of n, a(n) for n=0..20.

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);

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 February 18 15:08 EST 2018. Contains 299324 sequences. (Running on oeis4.)