OFFSET
2,3
COMMENTS
At least one block length occurs exactly 2 times, and all block lengths occur at most 2 times.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..648
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, 2)-b(n$2, 1):
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, 0, Min[k, n/i] }]]];
a[n_] := b[n, n, 2] - b[n, n, 1];
Table[a[n], {n, 2, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved