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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. Wagner, Asymptotic enumeration of extensional acyclic digraphs, in Proceedings of the SIAM Meeting on Analytic Algorithmics and Combinatorics (ANALCO12); http://siam.omnibooksonline.com/2012ANALCO/data/papers/001.pdf

LINKS

Table of n, a(n) for n=1..25.

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

CROSSREFS

Row sums give A182161. First column is A182163. Row lengths are A182220.

Sequence in context: A007764 A015195 A051421 * A258994 A110105 A182163

Adjacent sequences:  A182159 A182160 A182161 * A182163 A182164 A182165

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 15 2012

EXTENSIONS

a(15) - a(25) from Nathaniel Johnston, Apr 18 2012

STATUS

approved

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Last modified June 21 16:00 EDT 2018. Contains 305623 sequences. (Running on oeis4.)