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 A300353 #17 Mar 16 2025 03:58:49
%S A300353 1,1,0,1,1,2,2,4,7,14,24,46,92,186,368,750,1529,3160,6510,13590,28374,
%T A300353 59780,125732,266468,564188,1202842,2560106,5484304,11732400,25229068,
%U A300353 54187918,116938702,252039411,545593378,1179545874,2560009400,5550315640,12075064432
%N A300353 Number of strict trees of weight n with odd leaves.
%C A300353 This sequence is initially dominated by A300352 but eventually becomes much greater.
%C A300353 A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.
%H A300353 Andrew Howroyd, <a href="/A300353/b300353.txt">Table of n, a(n) for n = 0..500</a>
%F A300353 O.g.f: (1 + x/(1-x^2) + Product_{i>0} (1 + a(i)x^i))/2.
%F A300353 a(n) = Sum_{i=1..A000009(n)} A294018(A300351(n,i)).
%e A300353 The a(8) = 7 strict trees with odd leaves: (71), (53), (((51)1)1), (((31)3)1), (((31)1)3), ((31)31), (((((31)1)1)1)1).
%t A300353 d[n_]:=d[n]=If[EvenQ[n],0,1]+Sum[Times@@d/@y,{y,Select[IntegerPartitions[n],Length[#]>1&&UnsameQ@@#&]}];
%t A300353 Table[d[n],{n,40}]
%o A300353 (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n] = polcoef(x/(1-x^2) + prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)); concat([1], v)} \\ _Andrew Howroyd_, Aug 25 2018
%Y A300353 Cf. A000009, A063834, A078408, A089259, A196545, A279374, A279785, A289501, A294018, A294079, A299203, A300300, A300301, A300351, A300352, A300354, A300355.
%K A300353 nonn
%O A300353 0,6
%A A300353 _Gus Wiseman_, Mar 03 2018