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Number of labeled mating digraphs with n nodes.
(Formerly M3160)
6

%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