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A305552 Number of uniform normal multiset partitions of weight n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A126471 A317100 A199932 * A226652 A024696 A295360

Adjacent sequences:  A305549 A305550 A305551 * A305553 A305554 A305555

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 20 2018

STATUS

approved

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Last modified June 18 03:46 EDT 2021. Contains 345098 sequences. (Running on oeis4.)