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 A317084 #5 Jul 21 2018 10:05:37
%S A317084 1,1,1,2,2,4,4,6,7,10,11,16,17,23,27,34,38,50,54,70,79,97,107,135,148,
%T A317084 180,205,243,270,328,360,429,480,561,625,738,810,949,1057,1219,1349,
%U A317084 1571,1723,1986,2206,2515,2776,3188,3496,3983,4408,4980,5485,6228,6826
%N A317084 Number of integer partitions of n whose multiplicities are weakly increasing and span an initial interval of positive integers.
%e A317084 The a(7) = 6 integer partitions are (7), (61), (52), (43), (421), (331).
%t A317084 normalQ[m_]:=Union[m]==Range[Max[m]];
%t A317084 Table[Length[Select[IntegerPartitions[n],And[normalQ[Length/@Split[#]],OrderedQ[Reverse[Length/@Split[#]]]]&]],{n,60}]
%Y A317084 Cf. A000041, A000837, A055932, A242031, A317081, A317082, A317085, A317087, A317090.
%K A317084 nonn
%O A317084 0,4
%A A317084 _Gus Wiseman_, Jul 21 2018