OFFSET
0,3
FORMULA
a(n>0) = Sum_{d|n} binomial(2^(d-1),n/d).
EXAMPLE
The a(1) = 1 through a(4) = 9 sets:
{(1)} {(2)} {(3)} {(4)}
{(11)} {(12)} {(13)}
{(21)} {(22)}
{(111)} {(31)}
{(112)}
{(121)}
{(211)}
{(1111)}
{(2),(11)}
MATHEMATICA
Table[If[n==0, 1, Sum[Binomial[2^(d-1), n/d], {d, Divisors[n]}]], {n, 0, 30}]
PROG
(PARI) a(n) = if (n, sumdiv(n, d, binomial(2^(d-1), n/d)), 1); \\ Michel Marcus, Dec 14 2022
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 13 2022
STATUS
approved