A271736 Number of set partitions of [n] with maximal block length multiplicity equal to seven.

1, 0, 36, 120, 1320, 8712, 70356, 691119, 6628050, 55398200, 528441056, 5607882072, 55953959256, 559256993400, 6033783063160, 66852986570260, 743874599106485, 8455383000184208, 100088596628849400, 1202568046655647100, 14764362076427728050

Offset

7,3

Comments

At least one block length occurs exactly 7 times, and all block lengths occur at most 7 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 7..592

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, 7)-b(n$2, 6):
seq(a(n), n=7..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, 7] - b[n, n, 6];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=7 of A271423.

Sequence in context: A307939 A254146 A173420 * A280886 A278022 A333007

Adjacent sequences: A271733 A271734 A271735 * A271737 A271738 A271739

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved