The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A098407 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A098407

Number of different hierarchical orderings that can be formed from n unlabeled elements with no repetition of subhierarchies.
(history; published version)

#45 by Michael De Vlieger at Thu Dec 15 08:53:40 EST 2022

STATUS

proposed

approved

#44 by Gus Wiseman at Thu Dec 15 04:29:12 EST 2022

STATUS

editing

proposed

#43 by Gus Wiseman at Thu Dec 15 03:35:58 EST 2022

COMMENTS

a(n) is the number of finite sets of compositions with total sum n. The case of constant sums is A358904, cf. A074854. The case of distinct sums is A304961, ordered A336127. The ordered version (sequences of distinct compositions) is A358907. - Gus Wiseman, Dec 12 2022

CROSSREFS

Cf. A011782, A034691, A075729.

A001970 counts multisets of partitions.

Cf. A000009, A000041, A000219, A001970, A055887, A063834, A075900, A218482, A296122, A304961, A307068, A336342, A358836, A358912, `A358914.

#42 by Gus Wiseman at Tue Dec 13 03:03:42 EST 2022

COMMENTS

a(n) is the number of sets of compositions with total sum n. The case of constant sums is A358904, ordered cf. A074854. The case of distinct sums is A304961, ordered A336127. The ordered version (sequences of distinct compositions) is A358907. - Gus Wiseman, Dec 12 2022

#41 by Gus Wiseman at Mon Dec 12 09:30:49 EST 2022

COMMENTS

a(n) is the number of sets of compositions with total sum n. The case of constant sums is A358904, ordered A074854. The case of distinct sums is A304961, ordered A336127. The ordered version (sequences of distinct compositions) is A358907. - Gus Wiseman, Dec 12 2022

CROSSREFS

A001970 counts multisets of partitions.

A034691 counts multisets of compositions, ordered A133494.

A261049 counts sets of partitions, ordered A358906.

Cf. A000009, A000041, A000219, A055887, A063834, A075900, A218482, A296122, A304961, A307068, A336342, A358836, A358912, `A358914.

STATUS

approved

editing

#40 by Joerg Arndt at Sat Jan 11 00:35:26 EST 2020

STATUS

proposed

approved

#39 by Michel Marcus at Fri Jan 10 23:50:43 EST 2020

STATUS

editing

proposed

#38 by Michel Marcus at Fri Jan 10 23:50:39 EST 2020

FORMULA

a(n) = Sum_{ partitions n = s_1 + ... + s_n } Product_{ Set{s_i} } C(2^(s_i - 1), m(s_i)), where the sum runs over all partitions of n, the product runs over the set of parts of a given partition, s_i is the i-th part in the set of parts, C(k, l) denotes the binomial coefficient and m(s_i) is the multiplicity of part s_i in the given partition.

STATUS

proposed

editing

#37 by Jon E. Schoenfield at Fri Jan 10 23:08:40 EST 2020

STATUS

editing

proposed

#36 by Jon E. Schoenfield at Fri Jan 10 23:08:37 EST 2020

FORMULA

Sum_{ partitions n = s_1 + ... + s_n } Product_{ Set{s_i} } C(2^(s_i - 1), m(s_i)), where the sum runs over all partitions of n, the product runs over the set of parts of a given partition, s_i is the i-th part in the set of parts, C(k, l) denotes the binomial coefficient and m(s_i) is the multipliticity multiplicity of part s_i in the given partition.

STATUS

approved

editing