A086984 Number of arrangements of n labeled balls in n labeled columns where only 1 column may have more than 1 ball.

1, 6, 60, 696, 9120, 134640, 2227680, 41005440, 833172480, 18546796800, 449223667200, 11766674304000, 331501679308800, 9997170543360000, 321355745238528000, 10969253822951424000, 396269940892041216000

Offset

1,2

Comments

The difference between A000407 and A086984 is for example consider a(5). A000407 allows the 221 and 23 partitions, A086984 does not.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..402

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

Cf. A000407, A086985.

Sequence in context: A228484 A232969 A232246 * A000894 A112117 A065944

Adjacent sequences: A086981 A086982 A086983 * A086985 A086986 A086987

Keyword

nonn

Author

Jon Perry, Jul 27 2003

Status

approved