A086984 - OEIS

A086984

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

%I #15 Sep 14 2024 01:39:35

%S 1,6,60,696,9120,134640,2227680,41005440,833172480,18546796800,

%T 449223667200,11766674304000,331501679308800,9997170543360000,

%U 321355745238528000,10969253822951424000,396269940892041216000

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

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

%H Harvey P. Dale, <a href="/A086984/b086984.txt">Table of n, a(n) for n = 1..402</a>

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

%e a(2)=6;

%e .. .. -G -R R- G-

%e RG GR -R -G G- R-

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

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

%Y Cf. A000407, A086985.

%K nonn

%O 1,2

%A _Jon Perry_, Jul 27 2003