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

Offset: 0

Author

Gus Wiseman, Jun 20 2018

Keywords

• nonn

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.

Examples

			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}.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000005, A001315, A007716, A034691, A038041, A074854, A289078, A305552, A306017.

Programs

Mathematica

Table[Sum[Binomial[2^(n/k-1)+k-1,k],{k,Divisors[n]}],{n,35}]

PARI

a(n)={if(n<1, n==0, sumdiv(n, d, binomial(2^(n/d - 1) + d - 1, d)))} \\ Andrew Howroyd, Jun 22 2018

Formula

a(n) = Sum_{d|n} binomial(2^(n/d - 1) + d - 1, d).