A101819 - OEIS

%I #4 Mar 30 2012 18:57:06

%S 1,2,6,3,42,36,4,180,600,240,5,620,5400,7800,1800,6,1890,36120,12600,

%T 100800,15120,7,5334,202860,1428840,2646000,1340640,141120,8,14280,

%U 1016400,13053600,46710720,53343360,18627840,1451520,9,36792,4702320

%N Triangle read by rows: T(n,h) = number of functions f:{1,2,...,n}->{1,2,...,n-1} such that |Image(f)|=h, h=1,2,...,n-1, n=2,3,...

%F T(n, h) = C(n-1, h)*U(n, h), where U(n, h) is the array in A019538.

%e First rows:

%e 1

%e 2 6

%e 3 42 36

%e 4 180 600 240

%e To see that T(4,2)=42, first count 7 functions from {1,2,3,4}

%e onto {1,2} with f(1)=1 and 7 with f(1)=2. Count 14 onto {1,3}

%e and 14 onto {2,3}, for a total of 42.

%Y Cf. A019538, A101817, A101819, A101821.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Dec 17 2004