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).

1, 1, 3, 19, 1527, 16001, 2079863, 25138879, 3977502767, 9094756956909, 123064080712655, 323237794212444689, 63954318104304685581, 908009997951266138587, 185964440670918582766943, 563569187656087282078158821, 1764211191341056000567768115459

Offset

1,3

Links

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

Tamar Friedmann and John R. Harper, On H-Spaces and a Congruence of Catalan Numbers, arXiv preprint arXiv:1612.03837 [math.CO], 2016-2017.

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-François Alcover, Feb 20 2017 *)

Crossrefs

Cf. A000108, A000040.

Sequence in context: A192340 A326973 A248704 * A365579 A120563 A182344

Adjacent sequences: A098793 A098794 A098795 * A098797 A098798 A098799

Keyword

nonn

Author

F. Chapoton, Oct 05 2004

Status

approved