A182163 First column of A182162.

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

Offset

1,2

Links

Table of n, a(n) for n=1..15.

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

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 *)

Crossrefs

Cf. A182161, A182162, A001192.

Sequence in context: A182162 A258994 A110105 * A367052 A245358 A317350

Adjacent sequences: A182160 A182161 A182162 * A182164 A182165 A182166

Keyword

nonn

Author

N. J. A. Sloane, Apr 15 2012

Extensions

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

Status

approved