OFFSET
0,3
FORMULA
a(n) = Sum_{d|n} binomial(A000041(d),n/d).
EXAMPLE
The a(1) = 1 through a(6) = 14 sets:
{(1)} {(2)} {(3)} {(4)} {(5)} {(6)}
{(11)} {(21)} {(22)} {(32)} {(33)}
{(111)} {(31)} {(41)} {(42)}
{(211)} {(221)} {(51)}
{(1111)} {(311)} {(222)}
{(2),(11)} {(2111)} {(321)}
{(11111)} {(411)}
{(2211)}
{(3111)}
{(21111)}
{(111111)}
{(3),(21)}
{(3),(111)}
{(21),(111)}
MATHEMATICA
Table[If[n==0, 1, Sum[Binomial[PartitionsP[d], n/d], {d, Divisors[n]}]], {n, 0, 50}]
PROG
(PARI) a(n) = if (n, sumdiv(n, d, binomial(numbpart(d), n/d)), 1); \\ Michel Marcus, Dec 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 14 2022
STATUS
approved