This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359041 #10 Dec 14 2022 10:56:13
%S A359041 1,1,2,3,6,7,14,15,32,31,63,56,142,101,240,211,467,297,985,490,1524,
%T A359041 1247,2542,1255,6371,1979,7486,7070,14128,4565,32953,6842,42229,37863,
%U A359041 56266,17887,192914,21637,145820,197835,371853,44583,772740,63261,943966,1124840
%N A359041 Number of finite sets of integer partitions with all equal sums and total sum n.
%F A359041 a(n) = Sum_{d|n} binomial(A000041(d),n/d).
%e A359041 The a(1) = 1 through a(6) = 14 sets:
%e A359041 {(1)} {(2)} {(3)} {(4)} {(5)} {(6)}
%e A359041 {(11)} {(21)} {(22)} {(32)} {(33)}
%e A359041 {(111)} {(31)} {(41)} {(42)}
%e A359041 {(211)} {(221)} {(51)}
%e A359041 {(1111)} {(311)} {(222)}
%e A359041 {(2),(11)} {(2111)} {(321)}
%e A359041 {(11111)} {(411)}
%e A359041 {(2211)}
%e A359041 {(3111)}
%e A359041 {(21111)}
%e A359041 {(111111)}
%e A359041 {(3),(21)}
%e A359041 {(3),(111)}
%e A359041 {(21),(111)}
%t A359041 Table[If[n==0,1,Sum[Binomial[PartitionsP[d],n/d],{d,Divisors[n]}]],{n,0,50}]
%o A359041 (PARI) a(n) = if (n, sumdiv(n, d, binomial(numbpart(d), n/d)), 1); \\ _Michel Marcus_, Dec 14 2022
%Y A359041 This is the constant-sum case of A261049, ordered A358906.
%Y A359041 The version for all different sums is A271619, ordered A336342.
%Y A359041 Allowing repetition gives A305551, ordered A279787.
%Y A359041 The version for compositions instead of partitions is A358904.
%Y A359041 A001970 counts multisets of partitions.
%Y A359041 A034691 counts multisets of compositions, ordered A133494.
%Y A359041 A098407 counts sets of compositions, ordered A358907.
%Y A359041 Cf. A000005, A000041, A038041, A055887, A063834, A074854, A289078, A304961, A305552, A306017.
%K A359041 nonn
%O A359041 0,3
%A A359041 _Gus Wiseman_, Dec 14 2022