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

Author

Jon Perry, Jul 27 2003

Keywords

• nonn

Comments

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

Examples

			a(2)=6;
.. .. -G -R R- G-
RG GR -R -G G- R-
		

Links

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

Crossrefs

Cf. A000407, A086985.

Programs

Mathematica

Table[n!+Sum[Binomial[n-1,n-k],{k,2,n}]n n!,{n,20}] (* Harvey P. Dale, Nov 29 2019 *)

PARI

a(n)=n!+sum(i=2,n,binomial(n-1,n-i)*n*n!)

Formula

a(n) = n! + Sum_{i=2..n} binomial(n-1, n-i)*n*n!.