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A305874 Triangle lc(n,k): the number of purely line-connected k-partitions of [n], n>=4, 3<=k

%I A305874 #8 Apr 09 2020 19:32:22
%S A305874 1,6,2,24,20,3,81,128,45,4,250,672,417,84,5,732,3162,3090,1060,140,6,
%T A305874 2073,13908,20136,10476,2305,216,7,5742,58520,120900,89600,29225,4494,
%U A305874 315,8,15664,238832,686679,697224,316405,71016,8078,440,9
%N A305874 Triangle lc(n,k): the number of purely line-connected k-partitions of [n], n>=4, 3<=k<n.
%H A305874 T. Mansour and A. O. Munagi, <a href="http://dx.doi.org/10.1016/j.ejc.2009.07.001">Block-connected set partitions</a>, European J. Combin., 31 (2010), 887-902, Table 3.
%p A305874 A305874 := proc(n,k)
%p A305874     if n = k then
%p A305874         0;
%p A305874     elif n=k+1 then
%p A305874         k-2;
%p A305874     elif n >= k+1  then
%p A305874         k*procname(n-1,k)-procname(n-2,k)+(k-2)*combinat[stirling2](n-2,k-1) ;
%p A305874     else
%p A305874         0 ;
%p A305874     end if;
%p A305874 end proc:
%p A305874 for n from 4 to 12 do
%p A305874 for k from 3 to n-1 do
%p A305874     printf("%d,",A305874(n,k)) ;
%p A305874 end do:
%p A305874 printf("\n") ;
%p A305874 end do:
%Y A305874 Cf. A005564 (subdiagonal), A047790 (column k=3)
%K A305874 nonn,tabl,easy
%O A305874 4,2
%A A305874 _R. J. Mathar_, Jun 12 2018