A182163 First column of A182162.

1, 2, 12, 192, 8160, 898560, 245145600, 159035627520, 237882053283840, 802369403419852800, 6005354444640501350400, 98553538944200922572390400, 3514155297016560613680059596800, 270315783633381492859539110078054400, 44596108353446508026919663976179916800000

Offset: 1

Author

N. J. A. Sloane, Apr 15 2012

Keywords

• nonn

Links

• S. Wagner, Asymptotic enumeration of extensional acyclic digraphs, in Proceedings of the SIAM Meeting on Analytic Algorithmics and Combinatorics (ANALCO12).

Crossrefs

Cf. A182161, A182162, A001192.

Programs

Maple

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

Mathematica

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}]];
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}];
Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Apr 12 2023, after Nathaniel Johnston *)

Extensions

a(8)-a(15) and removal of a(0) from Nathaniel Johnston, Apr 18 2012