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 A002996 M3454 #43 Jul 02 2025 16:01:54
%S A002996 1,1,4,12,41,126,428,1416,4857,16753,58785,207868,742899,2674010,
%T A002996 9694799,35356240,129644789,477633711,1767263189,6564103612,
%U A002996 24466266587,91482504853,343059613649,1289903937896,4861946401410,18367352329251,69533550911142,263747949075908,1002242216651367
%N A002996 a(n) = Sum_{k|n} mu(k)*Catalan(n/k) (mu = Moebius function A008683).
%C A002996 Moebius transform of A000108.
%D A002996 A. Errera, Analysis situs - Un problème d'énumération, Mémoires Acad. Bruxelles, Classe des sciences, Série 2, Vol. XI, Fasc. 6, No. 1421 (1931), 26 pp.
%D A002996 A. Errera, De quelques problèmes d'analysis situs, Comptes Rend. Congr. Nat. Sci. Bruxelles, (1930), 106-110.
%D A002996 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002996 T. D. Noe, <a href="/A002996/b002996.txt">Table of n, a(n) for n=1..200</a>
%H A002996 A. Errera, <a href="https://academieroyale.be/fr/publications-academie-toutes-publications-detail/oeuvres-2/analysis-situs.-un-probleme-d-enumeration/">Analysis situs. Un problème d'énumération.</a>
%H A002996 A. Errera, <a href="/A002995/a002995.pdf">Reviews of two articles on Analysis Situs</a>, from Fortschritte [Annotated scanned copy]
%F A002996 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = 1/(1 - x/(1 - x/(1 - x/(1 - ...)))). - _Ilya Gutkovskiy_, May 06 2017
%t A002996 Table[Sum[MoebiusMu[k] CatalanNumber[n/k],{k,Divisors[n]}],{n,30}] (* _Harvey P. Dale_, Oct 07 2014 *)
%o A002996 (PARI) a(n)=sumdiv(n, d, moebius(n/d)*binomial(2*d,d)/(d+1)); \\ _Joerg Arndt_, Jun 15 2013
%o A002996 (Haskell)
%o A002996 a002996 n = sum $ zipWith (*) (map a008683 divs) (map a000108 $ reverse divs)
%o A002996 where divs = a027750_row n
%o A002996 -- _Reinhard Zumkeller_, Dec 22 2013
%Y A002996 Cf. A002995, A027750.
%K A002996 nonn,easy,nice
%O A002996 1,3
%A A002996 _N. J. A. Sloane_
%E A002996 More terms from _James Sellers_, Sep 08 2000
%E A002996 References corrected by _M. F. Hasler_, Aug 24 2012