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

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..576

Wikipedia, Partition of a set

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);

Crossrefs

Column k=3 of A319298.

Sequence in context: A158941 A128003 A060103 * A141989 A159512 A104132

Adjacent sequences: A332940 A332941 A332942 * A332944 A332945 A332946

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2020

Status

approved