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%I #13 Dec 14 2022 10:56:05
%S 1,1,2,4,9,16,38,64,156,260,632,1024,2601,4096,10208,16944,40966,
%T 65536,168672,262144,656980,1090240,2620928,4194304,10862100,16781584,
%U 41940992,69872384,168403448,268435456,693528552,1073741824,2695006177,4473400320,10737385472
%N Number of finite sets of compositions with all equal sums and total sum n.
%F a(n>0) = Sum_{d|n} binomial(2^(d-1),n/d).
%e The a(1) = 1 through a(4) = 9 sets:
%e {(1)} {(2)} {(3)} {(4)}
%e {(11)} {(12)} {(13)}
%e {(21)} {(22)}
%e {(111)} {(31)}
%e {(112)}
%e {(121)}
%e {(211)}
%e {(1111)}
%e {(2),(11)}
%t Table[If[n==0,1,Sum[Binomial[2^(d-1),n/d],{d,Divisors[n]}]],{n,0,30}]
%o (PARI) a(n) = if (n, sumdiv(n, d, binomial(2^(d-1), n/d)), 1); \\ _Michel Marcus_, Dec 14 2022
%Y This is the constant-sum case of A098407, ordered A358907.
%Y The version for distinct sums is A304961, ordered A336127.
%Y Allowing repetition gives A305552, ordered A074854.
%Y The case of sets of partitions is A359041.
%Y A001970 counts multisets of partitions.
%Y A034691 counts multisets of compositions, ordered A133494.
%Y A261049 counts sets of partitions, ordered A358906.
%Y Cf. A000009, A063834, A075900, A218482, A296122.
%K nonn
%O 0,3
%A _Gus Wiseman_, Dec 13 2022
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