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

1, 6, 2, 24, 20, 3, 81, 128, 45, 4, 250, 672, 417, 84, 5, 732, 3162, 3090, 1060, 140, 6, 2073, 13908, 20136, 10476, 2305, 216, 7, 5742, 58520, 120900, 89600, 29225, 4494, 315, 8, 15664, 238832, 686679, 697224, 316405, 71016, 8078, 440, 9

Offset

4,2

Links

Table of n, a(n) for n=4..48.

T. Mansour and A. O. Munagi, Block-connected set partitions, European J. Combin., 31 (2010), 887-902, Table 3.

Maple

A305874 := proc(n, k)
    if n = k then
        0;
    elif n=k+1 then
        k-2;
    elif n >= k+1  then
        k*procname(n-1, k)-procname(n-2, k)+(k-2)*combinat[stirling2](n-2, k-1) ;
    else
        0 ;
    end if;
end proc:
for n from 4 to 12 do
for k from 3 to n-1 do
    printf("%d, ", A305874(n, k)) ;
end do:
printf("\n") ;
end do:

Crossrefs

Cf. A005564 (subdiagonal), A047790 (column k=3)

Sequence in context: A090033 A036173 A142707 * A176965 A084249 A176591

Adjacent sequences: A305871 A305872 A305873 * A305875 A305876 A305877

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Jun 12 2018

Status

approved