A271734 Number of set partitions of [n] with maximal block length multiplicity equal to five.

1, 0, 21, 56, 504, 3717, 29337, 190674, 1460745, 12532520, 100025926, 845104624, 7657043576, 69364078980, 657324748866, 6374275533525, 64070264089020, 653567576544498, 6979149079277683, 74951288500334708, 835338959385664426, 9373747854520238761

Offset

5,3

Comments

At least one block length occurs exactly 5 times, and all block lengths occur at most 5 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 5..603

Wikipedia, Partition of a set

Maple

with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
        *b(n-i*j, i-1, k)/j!, j=0..min(k, n/i))))
    end:
a:= n-> b(n$2, 5)-b(n$2, 4):
seq(a(n), n=5..30);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, 0, Min[k, n/i] }]]];
a[n_] := b[n, n, 5] - b[n, n, 4];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=5 of A271423.

Sequence in context: A067727 A254144 A165237 * A189004 A183310 A280884

Adjacent sequences: A271731 A271732 A271733 * A271735 A271736 A271737

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved