A271735 Number of set partitions of [n] with maximal block length multiplicity equal to six.

1, 0, 28, 84, 840, 5082, 48279, 413127, 3093090, 26601575, 255431176, 2309491548, 20998179748, 209051155600, 2137087555220, 21652990622410, 230200208290745, 2517313465793819, 28104615964752327, 320432370881428575, 3760667223506993800, 45094960570293757695

Offset

6,3

Comments

At least one block length occurs exactly 6 times, and all block lengths occur at most 6 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 6..597

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, 6)-b(n$2, 5):
seq(a(n), n=6..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, 6] - b[n, n, 5];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A271423.

Sequence in context: A179790 A306427 A254145 * A280885 A042542 A042540

Adjacent sequences: A271732 A271733 A271734 * A271736 A271737 A271738

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved