|
| |
|
|
A122419
|
|
Number of labeled digraphs with n arcs and with no vertex of indegree 0.
|
|
3
| |
|
|
1, 0, 1, 8, 93, 1354, 23900, 496244, 11855700, 320428318, 9667220397, 322072882348, 11744421711587, 465270864839688, 19899234175413257, 913836170567749048, 44849438199960187278, 2342666125012348876152
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
FORMULA
| a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A122418(k). G.f.: Sum(((1+x)^(n-1)-1)^n,n=0..infinity).
|
|
|
MAPLE
| A122418 := proc(n) option remember ; add( combinat[stirling2](n, k)*(k-1)^n*k!, k=0..n) ; end: A122419 := proc(n) option remember ; add( combinat[stirling1](n, k)*A122418(k), k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, ", A122419(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
|
|
|
CROSSREFS
| Cf. A122420, A122400.
Sequence in context: A099291 A087579 A194043 * A121161 A098269 A010565
Adjacent sequences: A122416 A122417 A122418 * A122420 A122421 A122422
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 03 2006
|
|
|
EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
|
| |
|
|
