|
|
A055321
|
|
Number of labeled trees with n nodes and 9 leaves.
|
|
1
|
|
|
10, 28050, 12315600, 2501070000, 331387056000, 33590279923200, 2844207894528000, 212334102908928000, 14481281691676800000, 924652322084050560000, 56256869188969473024000, 3303981073122303974400000, 189156797595688810567680000, 10636600593905858347776000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
10,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n! * (n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400. - Vaclav Kotesovec, Jul 25 2014
|
|
MAPLE
|
a:= n-> (n!/9!)*Stirling2(n-2, n-9):
|
|
MATHEMATICA
|
Table[n! * (n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400, {n, 10, 25}] (* Vaclav Kotesovec, Jul 25 2014 *)
|
|
PROG
|
)$
for n : 10 thru 25 do
(PARI) A055321(n)={binomial(n, 9)*sum(i=0, n-=9, (-1)^i*binomial(n, i)*i^(n+7))*(-1)^n} /* or: Stirling2(n-2, n-9)*n!/9!, cf. A008277 */ /* M. F. Hasler, Mar 06 2012 */
(Magma) [Factorial(n)*(n-9)^2*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(9*n^4 - 270*n^3 + 2967*n^2 - 14098*n + 24352)/2106910310400: n in [10..25]]; // Vincenzo Librandi, Jul 25 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|