%I A138464
%S A138464 1,1,1,1,3,3,1,6,15,16,1,10,45,110,125,1,15,105,435,1080,1296,1,21,210,
%T A138464 1295,5250,13377,16807,1,28,378,3220,18865,76608,200704,262144,1,36,630,
%U A138464 7056,55755,320544,1316574,3542940,4782969,1,45,990,14070,143325
%N A138464 Triangle read by rows: T(n,k) = number of forests on n labeled nodes 
               with k edges (n>=1, 0<=k<=n-1).
%H A138464 Alois P. Heinz, <a href="b138464.txt">Table of n, a(n) for n = 1..1275</
               a>
%e A138464 Triangle begins:
%e A138464 1
%e A138464 1 1
%e A138464 1 3 3
%e A138464 1 6 15 16
%e A138464 1 10 45 110 125
%p A138464 T:= proc(n) option remember; if n=0 then 0 else T(n-1) +n^(n-1) *x^n/
               n! fi end: TT:= proc(n) option remember; expand (T(n) -T(n)^2/2) 
               end: f:= proc(k) option remember; if k=0 then 1 else unapply (f(k-1)(x) 
               +x^k/k!, x) fi end: A:= proc(n,k) option remember; series(f(k)(TT(n)), 
               x,n+1) end: aa:= (n,k)-> coeff (A(n,k), x,n) *n!: a:= (n,k)-> aa(n,
               n-k) -aa(n,n-k-1): seq (seq (a(n,k), k=0..n-1), n=1..10); [From Alois 
               P. Heinz (heinz(AT)hs-heilbronn.de), Sep 02 2008]
%Y A138464 Row sums give A001858. Rightmost diagonal gives A000272. Cf. A136605.
%Y A138464 Sequence in context: A094040 A039798 A001498 this_sequence A117279 A049323 
               A084144
%Y A138464 Adjacent sequences: A138461 A138462 A138463 this_sequence A138465 A138466 
               A138467
%K A138464 nonn,tabl
%O A138464 1,5
%A A138464 N. J. A. Sloane (njas(AT)research.att.com), May 09 2008
%E A138464 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 02 2008