|
|
A086984
|
|
Number of arrangements of n labeled balls in n labeled columns where only 1 column may have more than 1 ball.
|
|
2
|
|
|
1, 6, 60, 696, 9120, 134640, 2227680, 41005440, 833172480, 18546796800, 449223667200, 11766674304000, 331501679308800, 9997170543360000, 321355745238528000, 10969253822951424000, 396269940892041216000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n)=n!+sum(i=2, n, binomial(n-1, n-i)*n*n!)
|
|
EXAMPLE
|
a(2)=6;
.. .. -G -R R- G-
RG GR -R -G G- R-
|
|
MATHEMATICA
|
Table[n!+Sum[Binomial[n-1, n-k], {k, 2, n}]n n!, {n, 20}] (* Harvey P. Dale, Nov 29 2019 *)
|
|
PROG
|
(PARI) a(n)=n!+sum(i=2, n, binomial(n-1, n-i)*n*n!) for (i=2, 20, print1(a(i)", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|