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A182162
Triangle read by rows: number of extensional acyclic digraphs on n labeled nodes with k sources.
4
1, 2, 12, 192, 24, 8160, 2400, 898560, 384480, 14400, 245145600, 126040320, 9777600, 50400, 159035627520, 90043269120, 9660672000, 179222400, 80640, 237882053283840, 141969202744320, 17961178152960, 547498828800, 2586608640, 802369403419852800
OFFSET
1,2
LINKS
S. Wagner, Asymptotic enumeration of extensional acyclic digraphs, in Proceedings of the SIAM Meeting on Analytic Algorithmics and Combinatorics (ANALCO12).
EXAMPLE
Triangle begins:
1;
2;
12;
192, 24;
8160, 2400;
898560, 384480, 14400;
245145600, 126040320, 9777600, 50400;
...
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: A182162 := proc(n, l) local vl: vl := add((-1)^(k-l)*binomial(n, k)*binomial(k, l)*binomial(2^(n-k)-n+k, k)*k!*(n-k)!*A001192(n-k), k=l..n): if(vl = 0)then return NULL: fi: return vl: end: for n from 1 to 10 do seq(A182162(n, l), l=1..n); od; # 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}]];
A182162[n_, l_] := Module[{vl}, vl = Sum[(-1)^(k - l)* Binomial[n, k]*Binomial[k, l]*Binomial[2^(n - k) - n + k, k]*k!*(n - k)!*A001192[n - k], {k, l, n}]; If[vl == 0, Nothing, vl]];
Table[A182162[n, l], {n, 1, 10}, {l, 1, n}] // Flatten (* Jean-François Alcover, Mar 09 2023, after Nathaniel Johnston *)
CROSSREFS
Row sums give A182161. First column is A182163. Row lengths are A182220.
Sequence in context: A007764 A015195 A051421 * A258994 A110105 A182163
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Apr 15 2012
EXTENSIONS
a(15)-a(25) from Nathaniel Johnston, Apr 18 2012
STATUS
approved