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 A197432 #16 Jul 23 2017 21:55:44
%S A197432 0,1,1,2,2,3,3,4,5,6,6,7,7,8,8,9,14,15,15,16,16,17,17,18,19,20,20,21,
%T A197432 21,22,22,23,42,43,43,44,44,45,45,46,47,48,48,49,49,50,50,51,56,57,57,
%U A197432 58,58,59,59,60,61,62,62,63,63,64,64,65
%N A197432 a(n) = Sum_{k>=0} A030308(n,k)*C(k) where C(k) is the k-th Catalan number (A000108).
%C A197432 Replace 2^k with A000108(k) in binary expansion of n.
%F A197432 G.f.: (1/(1 - x))*Sum_{k>=0} Catalan number(k)*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jul 23 2017
%e A197432 11 = 1011_2, so a(11) = 1*1 + 1*1 + 0*2 + 1*5 = 7.
%Y A197432 Cf. A000108, A030308, A197433.
%Y A197432 Other sequences that are built by replacing 2^k in binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes), A197354 (odd numbers).
%K A197432 nonn,easy
%O A197432 0,4
%A A197432 _Philippe Deléham_, Oct 15 2011