login
A002996
a(n) = Sum_{k|n} mu(k)*Catalan(n/k) (mu = Moebius function A008683).
(Formerly M3454)
11
1, 1, 4, 12, 41, 126, 428, 1416, 4857, 16753, 58785, 207868, 742899, 2674010, 9694799, 35356240, 129644789, 477633711, 1767263189, 6564103612, 24466266587, 91482504853, 343059613649, 1289903937896, 4861946401410, 18367352329251, 69533550911142, 263747949075908, 1002242216651367
OFFSET
1,3
COMMENTS
Moebius transform of A000108.
REFERENCES
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.
A. Errera, De quelques problèmes d'analysis situs, Comptes Rend. Congr. Nat. Sci. Bruxelles, (1930), 106-110.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. Errera, Reviews of two articles on Analysis Situs, from Fortschritte [Annotated scanned copy]
FORMULA
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
MATHEMATICA
Table[Sum[MoebiusMu[k] CatalanNumber[n/k], {k, Divisors[n]}], {n, 30}] (* Harvey P. Dale, Oct 07 2014 *)
PROG
(PARI) a(n)=sumdiv(n, d, moebius(n/d)*binomial(2*d, d)/(d+1)); \\ Joerg Arndt, Jun 15 2013
(Haskell)
a002996 n = sum $ zipWith (*) (map a008683 divs) (map a000108 $ reverse divs)
where divs = a027750_row n
-- Reinhard Zumkeller, Dec 22 2013
CROSSREFS
Sequence in context: A149340 A246317 A180889 * A076867 A308369 A275184
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from James A. Sellers, Sep 08 2000
References corrected by M. F. Hasler, Aug 24 2012
STATUS
approved