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