This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302093 #32 May 12 2025 14:37:24
%S A302093 1,1,2,4,10,25,70,199,588,1784,5544,17569,56628,185202,613470,2054998,
%T A302093 6952660,23732911,81662152,283026021,987369656,3465222945,12228193432,
%U A302093 43369190282,154532114800,552998717472,1986841476000,7164993393905,25928281261800,94132464529902
%N A302093 a(n) = floor(C(n/2)*C(n/2+1)), where C = Catalan numbers (A000108).
%H A302093 Robert Israel, <a href="/A302093/b302093.txt">Table of n, a(n) for n = 0..1667</a>
%e A302093 k a(k) is prime
%e A302093 2 2
%e A302093 7 199
%e A302093 11 17569
%e A302093 17 23732911
%e A302093 81 102313363987695596246576033222404783284068513
%e A302093 619 200823128294216578246...307006792344011246479 (366 digits)
%p A302093 a108:= n -> binomial(2*n,n)/(n+1):
%p A302093 seq(floor(a108(n/2)*a108(n/2+1)),n=0..40); # _Robert Israel_, May 12 2025
%t A302093 Table[Floor[CatalanNumber[n/2] CatalanNumber[n/2 + 1]], {n, 0, 35}]
%Y A302093 Cf. A000108, A005568 (bisection, even part), A005817.
%K A302093 nonn
%O A302093 0,3
%A A302093 _Vincenzo Librandi_, Apr 11 2018