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A305874 Triangle lc(n,k): the number of purely line-connected k-partitions of [n], n>=4, 3<=k<n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

4,2

REFERENCES

T. Mansour, A. O. Munagi, Block-connected set partitions, Eur. J. Combinat. 31 (3) (2010) 887-902, Table 3. doi:10.1016/j.ejc.2009.07.001

LINKS

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

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

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Last modified January 17 18:02 EST 2020. Contains 330987 sequences. (Running on oeis4.)