A271762 Number of set partitions of [n] with minimal block length multiplicity equal to two.

1, 0, 3, 0, 55, 105, 945, 1218, 15456, 26785, 705573, 2502786, 32988670, 169561483, 1757881723, 10231748010, 84389906941, 540218433147, 6899156019034, 41756989590256, 554960234199955, 4793361957432730, 59690079139252499, 558283841454550850, 7093218105977514525

Offset: 2

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn

Examples

			a(4) = 3: 12|34, 13|24, 14|23.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..576
• Wikipedia, Partition of a set

Crossrefs

Column k=2 of A271424.

Programs

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, 2)-b(n$2, 3):
seq(a(n), n=2..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, 2] - b[n, n, 3];
Table[a[n], {n, 2, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Formula

a(n) = A271424(n,2).