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%I #15 Feb 20 2023 10:32:39
%S 1,1,3,19,1527,16001,2079863,25138879,3977502767,9094756956909,
%T 123064080712655,323237794212444689,63954318104304685581,
%U 908009997951266138587,185964440670918582766943,563569187656087282078158821,1764211191341056000567768115459
%N 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).
%H Tamar Friedmann and John R. Harper, <a href="http://arxiv.org/abs/1612.03837">On H-Spaces and a Congruence of Catalan Numbers</a>, arXiv preprint arXiv:1612.03837 [math.CO], 2016-2017.
%e a(4) = (132+1)/7 = 19.
%p with(numtheory): catalan_divise:=proc(n) (binomial(2*n-2,n-1)/n+1)/n end: seq(catalan_divise(ithprime(i)),i=1..20);
%t a[n_] := With[{p = Prime[n]}, (CatalanNumber[p-1]+1)/p]; Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Feb 20 2017 *)
%Y Cf. A000108, A000040.
%K nonn
%O 1,3
%A _F. Chapoton_, Oct 05 2004
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