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 A329740 #8 Nov 21 2019 22:14:53
%S A329740 1,1,1,1,4,7,4,10,10,10,73,196,133,379,319,379,502,805,562,1108,13648,
%T A329740 51448,51691,115174,140011,178597,203617,329737,292300,456703,456160,
%U A329740 608386,633466,898186,823009,39014392,190352269,266293795,493345615,834326995,947714938
%N A329740 Number of compositions of n whose multiplicities are distinct and cover an initial interval of positive integers.
%C A329740 A composition of n is a finite sequence of positive integers with sum n.
%e A329740 The a(1) = 1 through a(9) = 10 compositions:
%e A329740 (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e A329740 (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6) (1,1,7)
%e A329740 (1,2,1) (1,2,2) (1,4,1) (1,3,3) (1,6,1) (1,4,4)
%e A329740 (2,1,1) (1,3,1) (4,1,1) (1,5,1) (2,2,4) (1,7,1)
%e A329740 (2,1,2) (2,2,3) (2,3,3) (2,2,5)
%e A329740 (2,2,1) (2,3,2) (2,4,2) (2,5,2)
%e A329740 (3,1,1) (3,1,3) (3,2,3) (4,1,4)
%e A329740 (3,2,2) (3,3,2) (4,4,1)
%e A329740 (3,3,1) (4,2,2) (5,2,2)
%e A329740 (5,1,1) (6,1,1) (7,1,1)
%t A329740 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Range[Length[Union[#]]]==Sort[Length/@Split[Sort[#]]]&]],{n,0,10}]
%Y A329740 The version allowing repeated multiplicities is A329741.
%Y A329740 Complete compositions are A107429.
%Y A329740 Compositions whose multiplicities are distinct are A242882.
%Y A329740 Cf. A059966, A098504, A244164, A274174, A329739, A329766, A329748.
%K A329740 nonn
%O A329740 0,5
%A A329740 _Gus Wiseman_, Nov 21 2019
%E A329740 a(21)-a(40) from _Alois P. Heinz_, Nov 21 2019