cp's OEIS Frontend

A336139 Number of ways to choose a strict composition of each part of a strict composition of n.

%I A336139 #13 Jul 24 2020 22:18:33
%S A336139 1,1,1,5,9,17,45,81,181,397,965,1729,3673,7313,15401,34065,68617,
%T A336139 135069,266701,556969,1061921,2434385,4436157,9120869,17811665,
%U A336139 35651301,68949549,136796317,283612973,537616261,1039994921,2081261717,3980842425,7723253181,15027216049
%N A336139 Number of ways to choose a strict composition of each part of a strict composition of n.
%C A336139 A strict composition of n is a finite sequence of distinct positive integers summing to n.
%H A336139 Alois P. Heinz, <a href="/A336139/b336139.txt">Table of n, a(n) for n = 0..2000</a>
%e A336139 The a(1) = 1 through a(5) = 17 splittings:
%e A336139   (1)  (2)  (3)      (4)        (5)
%e A336139             (1,2)    (1,3)      (1,4)
%e A336139             (2,1)    (3,1)      (2,3)
%e A336139             (1),(2)  (1),(3)    (3,2)
%e A336139             (2),(1)  (3),(1)    (4,1)
%e A336139                      (1),(1,2)  (1),(4)
%e A336139                      (1),(2,1)  (2),(3)
%e A336139                      (1,2),(1)  (3),(2)
%e A336139                      (2,1),(1)  (4),(1)
%e A336139                                 (1),(1,3)
%e A336139                                 (1,2),(2)
%e A336139                                 (1),(3,1)
%e A336139                                 (1,3),(1)
%e A336139                                 (2),(1,2)
%e A336139                                 (2,1),(2)
%e A336139                                 (2),(2,1)
%e A336139                                 (3,1),(1)
%t A336139 strs[n_]:=Join@@Permutations/@Select[IntegerPartitions[n],UnsameQ@@#&];
%t A336139 Table[Length[Join@@Table[Tuples[strs/@ctn],{ctn,strs[n]}]],{n,0,15}]
%Y A336139 The version for partitions is A063834.
%Y A336139 Row sums of A072574.
%Y A336139 The version for non-strict compositions is A133494.
%Y A336139 The version for strict partitions is A279785.
%Y A336139 Multiset partitions of partitions are A001970.
%Y A336139 Strict compositions are A032020.
%Y A336139 Taking a composition of each part of a partition: A075900.
%Y A336139 Taking a composition of each part of a strict partition: A304961.
%Y A336139 Taking a strict composition of each part of a composition: A307068.
%Y A336139 Splittings of partitions are A323583.
%Y A336139 Compositions of parts of strict compositions are A336127.
%Y A336139 Set partitions of strict compositions are A336140.
%Y A336139 Cf. A318683, A318684, A319794, A336128, A336130, A336132.
%K A336139 nonn
%O A336139 0,4
%A A336139 _Gus Wiseman_, Jul 16 2020