A006025 Number of labeled mating digraphs with n nodes.

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

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

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.

Crossrefs

Cf. A006024.

Programs

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 *)

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

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

Extensions

More terms from Vladeta Jovovic, Feb 11 2003

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