A002996 a(n) = Sum_{k|n} mu(k)*Catalan(n/k) (mu = Moebius function A008683). (Formerly M3454)

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

T. D. Noe, Table of n, a(n) for n=1..200

A. Errera, Analysis situs. Un problème d'énumération.

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

Cf. A002995, A027750.

Sequence in context: A149340 A246317 A180889 * A076867 A308369 A275184

Adjacent sequences: A002993 A002994 A002995 * A002997 A002998 A002999

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Sep 08 2000

References corrected by M. F. Hasler, Aug 24 2012

Status

approved