A271764 Number of set partitions of [n] with minimal block length multiplicity equal to four.

1, 0, 0, 0, 105, 0, 0, 0, 67375, 135135, 1261260, 675675, 50925875, 97847750, 703993290, 6215737710, 228687298476, 58017429575, 11262925616250, 72813288304295, 2841531210935725, 11311740884766630, 252469888906590355, 2207276997956560530, 28579415631325499655

Offset

4,5

Links

Alois P. Heinz, Table of n, a(n) for n = 4..577

Wikipedia, Partition of a set

Formula

a(n) = A271424(n,4).

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, $k..n/i})))
    end:
a:= n-> b(n$2, 4)-b(n$2, 5):
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, Join[{0}, Range[k, n/i]]}]]];
a[n_] := b[n, n, 4] - b[n, n, 5];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=4 of A271424.

Sequence in context: A091539 A157874 A282188 * A069172 A231578 A104437

Adjacent sequences: A271761 A271762 A271763 * A271765 A271766 A271767

Keyword

nonn

Author

Alois P. Heinz, Apr 13 2016

Status

approved