A271738 Number of set partitions of [n] with maximal block length multiplicity equal to nine.

1, 0, 55, 220, 2860, 22022, 205205, 1853280, 17381650, 200982925, 2291851991, 23049864630, 262234646310, 3319690300850, 39333605649855, 464026283957060, 5880153732068000, 75836425964702975, 973764622911909400, 12796285021434965050, 173456578124336807300

Offset

9,3

Comments

At least one block length occurs exactly 9 times, and all block lengths occur at most 9 times.

Links

Alois P. Heinz, Table of n, a(n) for n = 9..586

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, 9)-b(n$2, 8):
seq(a(n), n=9..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, 9] - b[n, n, 8];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=9 of A271423.

Sequence in context: A294461 A013550 A254148 * A280888 A158658 A296036

Adjacent sequences: A271735 A271736 A271737 * A271739 A271740 A271741

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved