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A052830
A simple grammar: sequences of rooted cycles.
29
1, 0, 2, 3, 32, 150, 1524, 12600, 147328, 1705536, 23681520, 345605040, 5654922624, 98624766240, 1870594556544, 37794037488480, 817362198512640, 18742996919324160, 455648694329309184, 11683777530785978880, 315505598702787118080, 8943481464393674096640
OFFSET
0,3
COMMENTS
Asymptotic behavior (formula 3.2.) in the INRIA reference is wrong! - Vaclav Kotesovec, Jun 03 2019
LINKS
FORMULA
E.g.f.: 1/(1-x*log(1/(1-x))).
a(n) = (-1)^n*n!*Sum_{k=0..floor(n/2)} k!*Stirling1(n-k,k)/(n-k)!. - Vladimir Kruchinin, Nov 16 2011
a(n) ~ n! * r^(n+1)/(r+1/(r-1)), where r = 1.349976485401125... is the root of the equation (r-1)*exp(r) = r. - Vaclav Kotesovec, Sep 30 2013
a(0) = 1; a(n) = n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!. - Seiichi Manyama, May 04 2022
MAPLE
spec := [S, {B=Prod(C, Z), C=Cycle(Z), S=Sequence(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[1/(1+x*Log[1-x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)
PROG
(Maxima) a(n):=(-1)^(n)*n!*sum((k!*stirling1(n-k, k))/(n-k)!, k, 0, n/2); /* Vladimir Kruchinin, Nov 16 2011 */
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 1/(j-1)*v[i-j+1]/(i-j)!)); v; \\ Seiichi Manyama, May 04 2022
(PARI) a(n) = n!*sum(k=0, n\2, k!*abs(stirling(n-k, k, 1))/(n-k)!); \\ Seiichi Manyama, May 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Alois P. Heinz, Mar 16 2016
STATUS
approved