A271733 Number of set partitions of [n] with maximal block length multiplicity equal to four.

1, 0, 15, 35, 385, 2331, 13335, 88110, 629200, 4811235, 35992957, 276332420, 2325570065, 20036259075, 171879027000, 1583318184855, 14476456463826, 139849724906591, 1347082690705367, 13909222770509990, 144001190692525628, 1519193757875044900

Offset

4,3

Comments

At least one block length occurs exactly 4 times, and all block lengths occur at most 4 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 4..612

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, 4)-b(n$2, 3):
seq(a(n), n=4..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, 4] - b[n, n, 3];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=4 of A271423.

Sequence in context: A219689 A074891 A328213 * A280883 A306325 A241282

Adjacent sequences: A271730 A271731 A271732 * A271734 A271735 A271736

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved