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A006025 Number of labeled mating digraphs with n nodes.
(Formerly M3160)
6
1, 1, 3, 54, 3750, 1009680, 1058347920, 4375678520640, 71934792452208000, 4719774805970453006400, 1237727595442264073683462080, 1298006134163762816201615178698880, 5444432200219729912412940250057668378240 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. C. Read, The enumeration of mating-type graphs, Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989.
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2-k). - Vladeta Jovovic, Feb 11 2003
E.g.f.: Sum_{n>=0} 2^(n*(n-1))*log(1+x)^n/n!. - Paul D. Hanna, May 20 2009
MATHEMATICA
a[0] = 1; a[n_] := Sum[StirlingS1[n , k]*2^(k^2 - k), {k, 0, n}];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Aug 16 2019 *)
PROG
(PARI) a(n)=n!*polcoeff(sum(k=0, n, 2^(k*(k-1))*log(1+x+x*O(x^n))^k/k!), n) \\ Paul D. Hanna, May 20 2009
CROSSREFS
Cf. A006024.
Sequence in context: A091826 A091796 A171213 * A049414 A003027 A054545
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 11 2003
a(0)=1 prepended by Andrew Howroyd, Sep 09 2018
STATUS
approved

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Last modified February 24 13:52 EST 2024. Contains 370303 sequences. (Running on oeis4.)