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A101819 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,...

%I A101819 #4 Mar 30 2012 18:57:06
%S A101819 1,2,6,3,42,36,4,180,600,240,5,620,5400,7800,1800,6,1890,36120,12600,
%T A101819 100800,15120,7,5334,202860,1428840,2646000,1340640,141120,8,14280,
%U A101819 1016400,13053600,46710720,53343360,18627840,1451520,9,36792,4702320
%N A101819 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 A101819 T(n, h) = C(n-1, h)*U(n, h), where U(n, h) is the array in A019538.
%e A101819 First rows:
%e A101819 1
%e A101819 2 6
%e A101819 3 42 36
%e A101819 4 180 600 240
%e A101819 To see that T(4,2)=42, first count 7 functions from {1,2,3,4}
%e A101819 onto {1,2} with f(1)=1 and 7 with f(1)=2. Count 14 onto {1,3}
%e A101819 and 14 onto {2,3}, for a total of 42.
%Y A101819 Cf. A019538, A101817, A101819, A101821.
%K A101819 nonn,tabl
%O A101819 0,2
%A A101819 _Clark Kimberling_, Dec 17 2004