0,3

a(n) is the number of ways to seat n people at an unspecified number of circular tables and then linearly order the nonempty tables. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 18 2009]

Knopfmacher, A.; Ridley, J. N.; Reciprocal sums over partitions and compositions. SIAM J. Discrete Math. 6 (1993), no. 3, 388-399.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 122

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 119

Sum_{k=1}^{n} k!s(n, k), s(n, k) = unsigned Stirling number of first kind; E.g.f. 1/{1+log(1-z)}

For n>0, a(n) is the permanent of the n X n matrix with entries a(i, i) = i and a(i, j) = 1 elsewhere. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 09 2003

a(n) = A052860(n)/n for n>=1. a(n) = n!*Sum_{k=0..n-1} a(k)/k!/(n-k) for n>=1 with a(0)=1. - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006

E.g.f. is B(A(x)) where B(x)=1/(1-x) and A(x)=log[1/(1-x)] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 18 2009]

Table[Sum[Abs[StirlingS1[n, k]] k!, {k, 0, n}], {n, 0, 20}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 18 2009]

(PARI) a(n)=n!*polcoeff(1/(1+log(1-x +x*O(x^n))), n) - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006

Cf. A052860.

Sequence in context: A132624 A121587 A038170 this_sequence A007549 A081005 A074518

Adjacent sequences: A007837 A007838 A007839 this_sequence A007841 A007842 A007843

nonn

Arnold Knopfmacher [ ARNOLDK(AT)gauss.cam.wits.ac.za ]

Extended 6/95.