%I M3160 #31 Aug 16 2019 15:13:20
%S 1,1,3,54,3750,1009680,1058347920,4375678520640,71934792452208000,
%T 4719774805970453006400,1237727595442264073683462080,
%U 1298006134163762816201615178698880,5444432200219729912412940250057668378240
%N Number of labeled mating digraphs with n nodes.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A006025/b006025.txt">Table of n, a(n) for n = 0..50</a>
%H R. C. Read, <a href="https://oeis.org/A006023/a006023.pdf"> The enumeration of mating-type graphs</a>, Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989.
%F a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2-k). - _Vladeta Jovovic_, Feb 11 2003
%F E.g.f.: Sum_{n>=0} 2^(n*(n-1))*log(1+x)^n/n!. - _Paul D. Hanna_, May 20 2009
%t a[0] = 1; a[n_] := Sum[StirlingS1[n , k]*2^(k^2 - k), {k, 0, n}];
%t Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Aug 16 2019 *)
%o (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
%Y Cf. A006024.
%K nonn
%O 0,3
%A _Simon Plouffe_
%E More terms from _Vladeta Jovovic_, Feb 11 2003
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 09 2018