OFFSET
1,3
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, 1997. Proposition 1.3.16, p. 25.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..448
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
E.g.f.: (x-1+log(1-x)) / ( (x-1)^2 (log(1-x)-1) ).
a(n) = n!*(sum((-1)^(m)*(n-m+1)/(m-1)!*sum(k!*Stirling1(m-1,k),k,1,m-1),m,2,n)+1). - Vladimir Kruchinin, Sep 09 2010
a(n) ~ n!*n*(1 - 1/log(n) + gamma/log(n)^2), where gamma is Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Sep 25 2013
MATHEMATICA
Range[0, 21]!CoefficientList[ Series[(x - 1 + Log[1 - x])/((1 - x)^2(Log[1 - x] - 1)), {x, 0, 21}], x] (* Robert G. Wilson v, Jan 26 2007 *)
PROG
(Maxima) a(n):=n!*(sum((-1)^(m)*(n-m+1)/(m-1)!*sum(k!*stirling1(m-1, k), k, 1, m-1), m, 2, n)+1); /* Vladimir Kruchinin, Sep 09 2010 */
(PARI) x='x+O('x^30); Vec(serlaplace( (x-1+log(1-x))/((x-1)^2*(log(1-x) -1)))) \\ G. C. Greubel, Sep 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Wenjin Woan, Jan 17 2007
EXTENSIONS
More terms from N. J. A. Sloane, Jan 26 2007
STATUS
approved