%I A090657
%S A090657 1,0,1,0,2,2,0,3,18,6,0,4,84,144,24,0,5,300,1500,1200,120,0,6,930,10800,
%T A090657 23400,10800,720,0,7,2646,63210,294000,352800,105840,5040,0,8,7112,
%U A090657 324576,2857680,7056000,5362560,1128960,40320
%N A090657 Triangle read by rows: T(n,k) = number of functions from [1,2,...,n] 
               to [1,2,...,n] such that the image contains k elements (k in [1,2,
               ...,n]).
%C A090657 {1}, {0, 1}, {0, 2, 2}, {0, 3, 18, 6}, {0, 4, 84, 144, 24}, ...
%F A090657 T(n, k) = C(n, k)*A048993(n, k)*k! where A048993 = numbers of Stirling2. 
               T(n, k) = A008279(n, k) *A048993(n, k). T(n, k) = A019538(n, k)* 
               C(n, k) . Sum(k>=0, T(n, k)) = n^n; see A000312.
%F A090657 a(n,k) = k*a(n-1,k)*C(n,k)/C(n-1,k) + (n-(k-1))*a(n-1,k-1)*C(n,k-1)/C(n-1,
               k-1), with a(n,1) = n and a(n,n) = n! - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), 
               Nov 27 2006
%Y A090657 Cf. A007318 A048993 A019538 A08279 A000312.
%Y A090657 Sequence in context: A118262 A011137 A143396 this_sequence A108563 A138476 
               A131381
%Y A090657 Adjacent sequences: A090654 A090655 A090656 this_sequence A090658 A090659 
               A090660
%K A090657 easy,nonn,tabl
%O A090657 0,5
%A A090657 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 14 2003
%E A090657 Revised description from Jan Maciak, Apr 25 2004