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 A301765 #5 Mar 26 2018 20:03:39
%S A301765 1,1,2,2,3,3,4,5,8,7,11,11,19,16,27,23,42,33,63,47,87,71,119,90,195
%N A301765 Number of rooted twice-partitions of n where the first rooted partition is constant and the composite rooted partition is strict, i.e., of type (Q,R,Q).
%C A301765 A rooted partition of n is an integer partition of n - 1. A rooted twice-partition of n is a choice of a rooted partition of each part in a rooted partition of n.
%e A301765 The a(9) = 8 rooted twice-partitions:
%e A301765 (7), (61), (52), (43), (421),
%e A301765 (3)(21), (21)(3),
%e A301765 ()()()()()()()().
%t A301765 twirtns[n_]:=Join@@Table[Tuples[IntegerPartitions[#-1]&/@ptn],{ptn,IntegerPartitions[n-1]}];
%t A301765 Table[Select[twirtns[n],SameQ@@Total/@#&&UnsameQ@@Join@@#&]//Length,{n,20}]
%Y A301765 Cf. A002865, A032305, A063834, A093637, A127524, A279791, A296133, A301422, A301462, A301467, A301480, A301706.
%K A301765 nonn,more
%O A301765 1,3
%A A301765 _Gus Wiseman_, Mar 26 2018