OFFSET
0,3
COMMENTS
A multiset is normal if it spans an initial interval of positive integers. A multiset partition m is uniform if all parts have the same size, and normal if all parts are normal. The weight of m is the sum of sizes of its parts.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{d|n} binomial(2^(n/d - 1) + d - 1, d).
EXAMPLE
The a(4) = 12 uniform normal multiset partitions:
{1111}, {1222}, {1122}, {1112}, {1233}, {1223}, {1123}, {1234},
{11,11}, {11,12}, {12,12},
{1,1,1,1}.
MATHEMATICA
Table[Sum[Binomial[2^(n/k-1)+k-1, k], {k, Divisors[n]}], {n, 35}]
PROG
(PARI) a(n)={if(n<1, n==0, sumdiv(n, d, binomial(2^(n/d - 1) + d - 1, d)))} \\ Andrew Howroyd, Jun 22 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 20 2018
STATUS
approved