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 A244230 #20 Nov 18 2021 12:19:00
%S A244230 0,1,2,3,4,4,5,6,7,8,8,8,8,8,8,9,10,11,12,12,13,14,15,16,16,16,16,16,
%T A244230 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,18,19,20,20,21,22,23,
%U A244230 24,24,24,24,24,24,25,26,27,28,28,29,30,31,32,32,32,32
%N A244230 a(n) is the least k such that A197433(k) >= n.
%C A244230 For n >= 1, a(n) is the total number of ways the natural numbers in range 1 .. n can be represented as sums of distinct Catalan numbers (A000108). Note that for any one number, number of such solutions may be at most one. In other words, this sequence is one less than the partial sums of A176137 (number of partitions of n into distinct Catalan numbers).
%H A244230 Antti Karttunen, <a href="/A244230/b244230.txt">Table of n, a(n) for n = 0..6918</a>
%F A244230 For all n >= 0, a(A197433(n)) = n. [This works as an inverse function for the injection A197433].
%t A244230 nmax = 68;
%t A244230 A197433[n_] := If[n == 0, 0, SeriesCoefficient[(1/(1-x))*Sum[ CatalanNumber[k+1]*x^(2^k)/(1+x^(2^k)), {k, 0, Log[2, n] // Ceiling}], {x, 0, n}]];
%t A244230 a[n_] := For[k = 0, True, k++, If[A197433[k] >= n, Return[k]]];
%t A244230 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Nov 18 2021, after _Ilya Gutkovskiy_ in A197433 *)
%o A244230 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A244230 (define A244230 (LEAST-GTE-I 0 0 A197433))
%Y A244230 The first differences give A176137 from its term a(1) onward.
%Y A244230 Cf. A000108, A197433.
%K A244230 nonn
%O A244230 0,3
%A A244230 _Antti Karttunen_, Jun 25 2014