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