A006025 Number of labeled mating digraphs with n nodes. (Formerly M3160)

1, 1, 3, 54, 3750, 1009680, 1058347920, 4375678520640, 71934792452208000, 4719774805970453006400, 1237727595442264073683462080, 1298006134163762816201615178698880, 5444432200219729912412940250057668378240

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

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

Adjacent sequences: A006022 A006023 A006024 * A006026 A006027 A006028

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Vladeta Jovovic, Feb 11 2003

a(0)=1 prepended by Andrew Howroyd, Sep 09 2018

Status

approved