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 A349450 #27 Jul 23 2025 16:03:31
%S A349450 1,-1,-2,-4,-14,-38,-132,-420,-1426,-4834,-16796,-58688,-208012,
%T A349450 -742636,-2674384,-9693976,-35357670,-129641774,-477638700,
%U A349450 -1767253368,-6564119892,-24466233428,-91482563640,-343059494120,-1289904147128,-4861945985428,-18367353066440,-69533549429280,-263747951750360,-1002242211282032
%N A349450 Dirichlet inverse of right-shifted Catalan numbers [as when started from A000108(0): 1, 1, 2, 5, 14, 42, etc.].
%H A349450 Antti Karttunen, <a href="/A349450/b349450.txt">Table of n, a(n) for n = 1..1001</a>
%F A349450 a(1) = 1; a(n) = -Sum_{d|n, d < n} A000108((n/d)-1) * a(d).
%F A349450 For n > 1, a(n) = -A035010(n) = A035102(n) - A000108(n-1).
%F A349450 G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} Catalan(k-1) * A(x^k). - _Ilya Gutkovskiy_, Feb 23 2022
%F A349450 x = Sum_{n>=1} a(n) * C(x^n) where C(x) = (1 - sqrt(1-4*x))/2 is the g.f. of the Catalan numbers (A000108). - _Paul D. Hanna_, Nov 27 2024
%t A349450 a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#] * CatalanNumber[n/# - 1] &, # < n &]; Array[a, 30] (* _Amiram Eldar_, Nov 22 2021 *)
%o A349450 (PARI)
%o A349450 A000108(n) = binomial(2*n, n)/(n+1);
%o A349450 memoA349450 = Map();
%o A349450 A349450(n) = if(1==n,1,my(v); if(mapisdefined(memoA349450,n,&v), v, v = -sumdiv(n,d,if(d<n,A000108((n/d)-1)*A349450(d),0)); mapput(memoA349450,n,v); (v)));
%Y A349450 Cf. A000108, A035010, A035102.
%Y A349450 Cf. also A349449, A349451, A349452, A349453, A349564.
%K A349450 sign
%O A349450 1,3
%A A349450 _Antti Karttunen_, Nov 22 2021