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%I #7 Nov 29 2019 13:53:25
%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!) for (i=2,20,print1(a(i)","))
%Y Cf. A000407, A086985.
%K nonn
%O 1,2
%A _Jon Perry_, Jul 27 2003
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