|
| |
|
|
A053530
|
|
E.g.f.: exp(-x-1/2*x^2+x*exp(x)).
|
|
1
| |
|
|
1, 0, 1, 3, 7, 35, 171, 847, 5041, 32643, 223705, 1659581, 13182159, 110802133, 984241363, 9212696235, 90477239521, 929604133343, 9969157068273, 111329454692485, 1291932988047775, 15550838026589061, 193833398512358011, 2498039016973836491
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| The number of simple labelled graphs on n nodes whose connected compomnents are stars. - Geoffrey Critzer, Dec 10 2011
|
|
|
REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(b).
|
|
|
LINKS
| Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
|
|
|
FORMULA
| a(n)=n!*sum((binomial(k,n-k)*2^(k-n)*(-1)^k+sum(binomial(k,j)*sum(j^(i-j)/(i-j)!*binomial(k-j,n-i-k+j)*(1/2)^(n-i-k+j)*(-1)^(k-j),i,j,n-k+j),j,1,k))/k!,k,1,n), n>0. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
|
|
|
MATHEMATICA
| nn = 16; a = x Exp[x]; Range[0, nn]! CoefficientList[Series[Exp[a - x^2/2! - x], {x, 0, nn}], x] (* Geoffrey Critzer, Dec 10 2011 *)
|
|
|
PROG
| (Other) a(n):=n!*sum((binomial(k, n-k)*2^(k-n)*(-1)^k+sum(binomial(k, j)*sum(j^(i-j)/(i-j)!*binomial(k-j, n-i-k+j)*(1/2)^(n-i-k+j)*(-1)^(k-j), i, j, n-k+j), j, 1, k))/k!, k, 1, n); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
|
|
|
CROSSREFS
| Cf. A000248
Sequence in context: A055487 A121130 A006099 * A132102 A081555 A027624
Adjacent sequences: A053527 A053528 A053529 * A053531 A053532 A053533
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 16 2000
|
| |
|
|
