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 A301706 #4 Mar 26 2018 20:02:19
%S A301706 1,1,2,4,9,19,43,91,201,422,918,1896,4089,8376,17793,36445,76446,
%T A301706 155209,324481,655426,1355220,2741092,5617505,11291037,23086423,
%U A301706 46227338,93753196,187754647,378675055,754695631,1518414812,3016719277,6037006608,11984729983
%N A301706 Number of rooted thrice-partitions of n.
%C A301706 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. A rooted thrice-partition of n is a choice of a rooted twice-partition of each part in a rooted partition of n.
%e A301706 The a(5) = 9 rooted thrice-partitions:
%e A301706 ((2)), ((11)), ((1)()), (()()()),
%e A301706 ((1))(), (()())(), (())(()),
%e A301706 (())()(),
%e A301706 ()()()().
%e A301706 The a(6) = 19 rooted thrice-partitions:
%e A301706 ((3)), ((21)), ((111)), ((2)()), ((11)()), ((1)(1)), ((1)()()), (()()()()),
%e A301706 ((2))(), ((11))(), ((1)())(), (()()())(), ((1))(()), (()())(()),
%e A301706 ((1))()(), (()())()(), (())(())(),
%e A301706 (())()()(),
%e A301706 ()()()()().
%t A301706 twire[n_]:=twire[n]=Sum[Times@@PartitionsP/@(ptn-1),{ptn,IntegerPartitions[n-1]}];
%t A301706 thrire[n_]:=Sum[Times@@twire/@ptn,{ptn,IntegerPartitions[n-1]}];
%t A301706 Array[thrire,30]
%Y A301706 Cf. A000041, A001383, A002865, A063834, A093637, A119442, A196545, A281113, A289501, A300383, A301422, A301462, A301467, A301480, A301595, A301598.
%K A301706 nonn
%O A301706 1,3
%A A301706 _Gus Wiseman_, Mar 25 2018