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A098796 a(n) = (Catalan(P_n-1)+1)/P_n where P_n is the n-th prime and Catalan(k) is the Catalan number binomial(2k, k)/(k+1). 0
1, 1, 3, 19, 1527, 16001, 2079863, 25138879, 3977502767, 9094756956909, 123064080712655, 323237794212444689, 63954318104304685581, 908009997951266138587, 185964440670918582766943, 563569187656087282078158821, 1764211191341056000567768115459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..17.

Tamar Friedmann, JR Harper, On H-Spaces and a Congruence of Catalan Numbers, arXiv preprint arXiv:1612.03837, 2016

EXAMPLE

a(4) = (132+1)/7 = 19.

MAPLE

with(numtheory): catalan_divise:=proc(n) (binomial(2*n-2, n-1)/n+1)/n end: seq(catalan_divise(ithprime(i)), i=1..20);

MATHEMATICA

a[n_] := With[{p = Prime[n]}, (CatalanNumber[p-1]+1)/p]; Table[a[n], {n, 1, 15}] (* Jean-Fran├žois Alcover, Feb 20 2017 *)

CROSSREFS

Cf. A000108, A000040.

Sequence in context: A258669 A192340 A248704 * A120563 A182344 A191623

Adjacent sequences:  A098793 A098794 A098795 * A098797 A098798 A098799

KEYWORD

nonn

AUTHOR

F. Chapoton, Oct 05 2004

STATUS

approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)