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 A218441 #26 Apr 26 2025 03:27:47
%S A218441 1,1,6,60,770,11466,188496,3325608,61866090,1199333850,24030289140,
%T A218441 494663027040,10414559269296,223487031938800,4874879691748800,
%U A218441 107852781825352080,2415945569351185530,54714061423541554650,1251237165698155135500,28864572348777684057000
%N A218441 a(n) = A000108(n)*A001764(n).
%C A218441 G.f. of A000108, C(x), satisfies: C(x) = 1 + x*C(x)^2;
%C A218441 G.f. of A001764, F(x), satisfies: F(x) = 1 + x*F(x)^3.
%H A218441 Amiram Eldar, <a href="/A218441/b218441.txt">Table of n, a(n) for n = 0..705</a>
%F A218441 a(n) ~ 3^(3*n+1/2)/(2*Pi*n*(n+1)*(2*n+1)) = A086201*3^(3*n+1/2)/(n*(n+1)*(2*n+1)) (using the Stirling approximation for n!). - _A.H.M. Smeets_, Dec 31 2022
%e A218441 G.f.: A(x) = 1 + x + 6*x^2 + 60*x^3 + 770*x^4 + 11466*x^5 + 188496*x^6 + ...
%t A218441 a[n_] := CatalanNumber[n] * Binomial[3*n, n]/(2*n+1); Array[a, 20, 0] (* _Amiram Eldar_, Apr 26 2025 *)
%o A218441 (PARI) {a(n)=binomial(2*n,n)/(n+1)*binomial(3*n,n)/(2*n+1)}
%o A218441 for(n=0,25,print1(a(n),", "))
%o A218441 (Maxima) A218441[n]:=binomial(2*n, n)/(n+1)*binomial(3*n, n)/(2*n+1)$
%o A218441 makelist(A218441[n],n,0,30); /* _Martin Ettl_, Oct 29 2012 */
%Y A218441 Cf. A000108, A001764, A086201.
%K A218441 nonn,easy
%O A218441 0,3
%A A218441 _Paul D. Hanna_, Oct 28 2012