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 A379099 #6 Dec 15 2024 10:07:09
%S A379099 1,3,18,145,1386,14742,168300,2019303,25135110,321849814,4215006588,
%T A379099 56222048610,761436454492,10446021648900,144895117640040,
%U A379099 2029085114629545,28652994844093170,407600869429602090,5836323240704117700,84058779645184757490,1217059539049881032220
%N A379099 a(n) = Sum_{k=0..n} binomial(2*k, k)*binomial(2*n, n)/(n + 1). Row sums of A379100.
%F A379099 a(n) = CatalanNumber(n)*binomial(2*n, n)*hypergeom([1, -n], [1/2 - n], 1/4).
%F A379099 a(n) = A000108(n) * A006134(n).
%p A379099 CatalanNumber := n -> binomial(2*n, n)/(n + 1):
%p A379099 a := n -> CatalanNumber(n)*binomial(2*n, n)*hypergeom([1, -n], [1/2 - n], 1/4):
%p A379099 seq(simplify(a(n)), n = 0..20);
%Y A379099 Cf. A000108, A000984, A006134, A379100.
%K A379099 nonn
%O A379099 0,2
%A A379099 _Peter Luschny_, Dec 15 2024