|
Search: id:A001784
|
|
|
| A001784 |
|
Second order reciprocal Stirling number (Fekete) [[2n+3 \over n]]. The number of n-orbit permutations of a (2n+3)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M5169 N2244)
|
|
+0
4
|
|
| 1, 24, 924, 26432, 705320, 18858840, 520059540, 14980405440, 453247114320, 14433720701400, 483908513388300, 17068210823664000, 632607429473019000, 24602295329058447000, 1002393959071727722500, 42720592574082543120000
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.
|
|
FORMULA
|
[[2n+3, n]]=sum((-1)^i*binomial(2n+3, 2n+3-i)[2n+3-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
|
|
MAPLE
|
with(combinat):s1 := (n, k)->sum((-1)^i*binomial(n, i)*abs(stirling1(n-i, k-i)), i=0..n); for j from 1 to 20 do s1(2*j+3, j); od;
|
|
CROSSREFS
|
Cf. A000907, A000483, A001785.
Sequence in context: A107391 A006147 A061236 this_sequence A001866 A033590 A006175
Adjacent sequences: A001781 A001782 A001783 this_sequence A001785 A001786 A001787
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms, Maple program, formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
|
|
|
Search completed in 0.002 seconds
|
