A271737 Number of set partitions of [n] with maximal block length multiplicity equal to eight.

1, 0, 45, 165, 1980, 14157, 123123, 1042470, 11229075, 117721175, 1085614101, 11354532696, 132028149240, 1440550986525, 15693895739115, 183700174158435, 2200557929261230, 26295830857171150, 323510486572841425, 4085513198322259275, 52716487743732737925

Offset

8,3

Comments

At least one block length occurs exactly 8 times, and all block lengths occur at most 8 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 8..588

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, 8)-b(n$2, 7):
seq(a(n), n=8..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, 8] - b[n, n, 7];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=8 of A271423.

Sequence in context: A305069 A061658 A254147 * A280887 A158630 A158634

Adjacent sequences: A271734 A271735 A271736 * A271738 A271739 A271740

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved