A305552 - OEIS

A305552

Number of uniform normal multiset partitions of weight n.

1, 1, 3, 5, 12, 17, 47, 65, 170, 277, 655, 1025, 2739, 4097, 10281, 17257, 41364, 65537, 170047, 262145, 660296, 1094457, 2621965, 4194305, 10898799, 16792721, 41945103, 69938141, 168546184, 268435457, 694029255, 1073741825, 2696094037, 4474449261, 10737451027

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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