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 A332272 #7 Mar 09 2020 18:25:24
%S A332272 1,1,2,3,5,6,8,10,14,18,23,30,37,46,52,70,80,100,116,146,171,203,236,
%T A332272 290,332,401,458,547,626,744,851,1004,1157,1353,1553,1821,2110,2434,
%U A332272 2810,3250,3741,4304,4949,5661,6510,7450,8501,9657,11078,12506,14329,16185
%N A332272 Number of narrowly recursively normal integer partitions of n.
%C A332272 A sequence is narrowly recursively normal if either it is constant (narrow) or its run-lengths are a narrowly recursively normal sequence covering an initial interval of positive integers (normal).
%F A332272 For n > 1, a(n) = A317491(n) + A000005(n) - 2.
%e A332272 The a(6) = 8 partitions are (6), (51), (42), (411), (33), (321), (222), (111111). Missing from this list are (3111), (2211), (21111).
%e A332272 The a(1) = 1 through a(8) = 14 partitions:
%e A332272 (1) (2) (3) (4) (5) (6) (7) (8)
%e A332272 (11) (21) (22) (32) (33) (43) (44)
%e A332272 (111) (31) (41) (42) (52) (53)
%e A332272 (211) (221) (51) (61) (62)
%e A332272 (1111) (311) (222) (322) (71)
%e A332272 (11111) (321) (331) (332)
%e A332272 (411) (421) (422)
%e A332272 (111111) (511) (431)
%e A332272 (3211) (521)
%e A332272 (1111111) (611)
%e A332272 (2222)
%e A332272 (3221)
%e A332272 (4211)
%e A332272 (11111111)
%t A332272 normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
%t A332272 recnQ[ptn_]:=With[{qtn=Length/@Split[ptn]},Or[Length[qtn]<=1,And[normQ[qtn],recnQ[qtn]]]];
%t A332272 Table[Length[Select[IntegerPartitions[n],recnQ]],{n,0,30}]
%Y A332272 The strict instead of narrow version is A330937.
%Y A332272 The normal case is A332277.
%Y A332272 The widely normal case is A332277(n) - 1 for n > 1.
%Y A332272 The wide version is A332295(n) - 1.
%Y A332272 Cf. A000009, A107429, A181819, A316496, A317081, A317245, A317491, A329744, A329746, A329766, A332576.
%K A332272 nonn
%O A332272 0,3
%A A332272 _Gus Wiseman_, Mar 08 2020