A332943 Number of entries in the third blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 13, 71, 396, 1877, 9199, 47371, 253108, 1420475, 8598976, 55100124, 369764734, 2614650820, 19473708445, 151503397725, 1226996194292, 10339319950504, 90530421514787, 821670728202320, 7714779905351852, 74815825933883534, 748526174347790448, 7717807072187843156

Offset: 3

Author

Alois P. Heinz, Mar 03 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..576
• Wikipedia, Partition of a set

Crossrefs

Column k=3 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, 3)[2]:
seq(a(n), n=3..25);