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%I #16 Apr 12 2023 08:56:31
%S 1,2,12,192,8160,898560,245145600,159035627520,237882053283840,
%T 802369403419852800,6005354444640501350400,98553538944200922572390400,
%U 3514155297016560613680059596800,270315783633381492859539110078054400,44596108353446508026919663976179916800000
%N First column of A182162.
%H S. Wagner, <a href="http://math.sun.ac.za/swagner/DigraphsFull.pdf">Asymptotic enumeration of extensional acyclic digraphs</a>, in Proceedings of the SIAM Meeting on Analytic Algorithmics and Combinatorics (ANALCO12).
%p A001192 := proc(n) option remember: if(n=0)then return 1: fi: return add((-1)^(n-k-1)*binomial(2^k-k,n-k)*procname(k), k=0..n-1); end: A182163 := proc(n) return add((-1)^(k-1)*k*binomial(n,k)*binomial(2^(n-k)-n+k,k)*k!*(n-k)!*A001192(n-k), k=1..n): end: seq(A182163(n), n=1..16); # _Nathaniel Johnston_, Apr 18 2012
%t A001192[n_] := A001192[n] = If[n == 0, 1, Sum[(-1)^(n - k - 1)*Binomial[2^k - k, n - k]*A001192[k], {k, 0, n - 1}]];
%t a[n_] := Sum[(-1)^(k - 1)*Binomial[n, k]*k*Binomial[2^(n - k) - n + k, k]*k!*(n - k)!*A001192[n - k], {k, 1, n}];
%t Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Apr 12 2023, after _Nathaniel Johnston_ *)
%Y Cf. A182161, A182162, A001192.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 15 2012
%E a(8)-a(15) and removal of a(0) from _Nathaniel Johnston_, Apr 18 2012
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