|
| |
|
|
A006025
|
|
Number of labeled mating digraphs with n nodes.
(Formerly M3160)
|
|
4
| |
|
|
1, 3, 54, 3750, 1009680, 1058347920, 4375678520640, 71934792452208000, 4719774805970453006400, 1237727595442264073683462080, 1298006134163762816201615178698880, 5444432200219729912412940250057668378240
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| R. C. Read, The Enumeration of Mating-Type Graphs. Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| a(n) = Sum_{k=0..n} stirling1(n, k)*2^(k^2-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
E.g.f.: -1 + Sum_{n>=0} 2^(n(n-1))*log(1+x)^n/n!. [From Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009]
|
|
|
PROG
| (PARI) a(n)=n!*polcoeff(sum(k=0, n, 2^(k*(k-1))*log(1+x+x*O(x^n))^k/k!), n) [From Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009]
|
|
|
CROSSREFS
| Cf. A006024.
Sequence in context: A091826 A091796 A171213 * A049414 A003027 A054545
Adjacent sequences: A006022 A006023 A006024 * A006026 A006027 A006028
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
|
|
|
EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 11 2003
|
| |
|
|
