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

Author

F. Chapoton, Oct 05 2004

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000108, A000040.

Programs

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 *)