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 A329748 #7 Jul 06 2020 20:07:25
%S A329748 1,1,0,2,3,3,6,12,12,42,114,210,60,360,720,1320,1590,3690,6450,16110,
%T A329748 33120,59940,61320,112980,171780,387240,803880,769440,1773240,2823240,
%U A329748 5790960,9916200,19502280,28244160,56881440,130548600,279578880,320554080,541323720
%N A329748 Number of complete compositions of n whose multiplicities cover an initial interval of positive integers.
%C A329748 A composition of n is a finite sequence of positive integers with sum n. It is complete if it covers an initial interval of positive integers.
%e A329748 The a(1) = 1 through a(8) = 12 compositions (empty column not shown):
%e A329748 (1) (12) (112) (122) (123) (1123) (1223)
%e A329748 (21) (121) (212) (132) (1132) (1232)
%e A329748 (211) (221) (213) (1213) (1322)
%e A329748 (231) (1231) (2123)
%e A329748 (312) (1312) (2132)
%e A329748 (321) (1321) (2213)
%e A329748 (2113) (2231)
%e A329748 (2131) (2312)
%e A329748 (2311) (2321)
%e A329748 (3112) (3122)
%e A329748 (3121) (3212)
%e A329748 (3211) (3221)
%t A329748 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A329748 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],normQ[#]&&normQ[Length/@Split[Sort[#]]]&]],{n,0,10}]
%Y A329748 Looking at run-lengths instead of multiplicities gives A329749.
%Y A329748 The non-complete version is A329741.
%Y A329748 Complete compositions are A107429.
%Y A329748 Cf. A008965, A098504, A244164, A274174, A329740, A329744, A329766.
%K A329748 nonn
%O A329748 0,4
%A A329748 _Gus Wiseman_, Nov 21 2019
%E A329748 a(21)-a(38) from _Alois P. Heinz_, Jul 06 2020