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 A305552 Number of uniform normal multiset partitions of weight n. 1

%I

%S 1,1,3,5,12,17,47,65,170,277,655,1025,2739,4097,10281,17257,41364,

%T 65537,170047,262145,660296,1094457,2621965,4194305,10898799,16792721,

%U 41945103,69938141,168546184,268435457,694029255,1073741825,2696094037,4474449261,10737451027

%N Number of uniform normal multiset partitions of weight n.

%C 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.

%H Andrew Howroyd, <a href="/A305552/b305552.txt">Table of n, a(n) for n = 0..1000</a>

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

%e The a(4) = 12 uniform normal multiset partitions:

%e {1111}, {1222}, {1122}, {1112}, {1233}, {1223}, {1123}, {1234},

%e {11,11}, {11,12}, {12,12},

%e {1,1,1,1}.

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

%o (PARI) a(n)={if(n<1, n==0, sumdiv(n, d, binomial(2^(n/d - 1) + d - 1, d)))} \\ _Andrew Howroyd_, Jun 22 2018

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

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 20 2018

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Last modified July 28 11:14 EDT 2021. Contains 346326 sequences. (Running on oeis4.)