%I A143396
%S A143396 1,0,1,0,2,2,0,3,9,5,0,4,30,40,15,0,5,90,220,185,52,0,6,255,1040,1485,
%T A143396 906,203,0,7,693,4550,9905,9891,4718,877,0,8,1820,19040,59850,87416,
%U A143396 66808,26104,4140,0,9,4644,77448,341082,686826,750120,463212,153063
%N A143396 Triangle T(n,k)=number of forests of labeled rooted trees of height at 
               most 1, with n labels, k of which are used for root nodes and any 
               root may contain >= 1 labels, n >= 0, 0<=k<=n.
%H A143396 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A143396 T(n, k) = binomial(n,k) * Sum_{t=0..k} stirling2(k,t)*t^(n-k).
%F A143396 E.g.f.: exp(exp(x)*(exp(x*y)-1)). [From Vladeta Jovovic (vladeta(AT)eunet.yu), 
               Dec 08 2008]
%e A143396 T (3,2) = 9: {1,2}<-3, {1,3}<-2, {2,3}<-1, {1}<-3{2}, {1}{2}<-3, {1}<-2{3}, 
               {1}{3}<-2, {2}<-1{3}, {2}{3}<-1.
%e A143396 Triangle begins:
%e A143396 [1]
%e A143396 [0, 1]
%e A143396 [0, 2, 2]
%e A143396 [0, 3, 9, 5]
%e A143396 [0, 4, 30, 40, 15]
%p A143396 with (combinat,stirling2): T := (n,k)-> binomial(n,k)* sum(stirling2(k,
               t)* t^(n-k), t=0..k); seq (seq (T(n, k), k=0..n), n=0..11);
%Y A143396 Columns k=0-1: A000007, A000027. Diagonal: A000110. See also A048993, 
               A008277, A007318, A143405 for row sums.
%Y A143396 Sequence in context: A065484 A118262 A011137 this_sequence A090657 A108563 
               A138476
%Y A143396 Adjacent sequences: A143393 A143394 A143395 this_sequence A143397 A143398 
               A143399
%K A143396 nonn,tabl
%O A143396 0,5
%A A143396 Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 12 2008