A332947 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 57, 1045, 16126, 207131, 2351933, 24592218, 244969609, 2361155669, 22194089013, 205472269667, 1894376413748, 17523281149447, 163348288354057, 1541060427442896, 14781379209476531, 144692817107094283, 1449416720608086968, 14882752251954912426

Offset: 7

Author

Alois P. Heinz, Mar 03 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..576
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A319298.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
      max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
    end:
a:= n-> b(n, 1, 7)[2]:
seq(a(n), n=7..25);