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 A262394 #18 Nov 10 2022 07:42:51
%S A262394 1,4,20,110,637,3808,23256,144210,904475,5722860,36463440,233646504,
%T A262394 1504152860,9721421440,63040282096,409972529754,2672860120455,
%U A262394 17464206951100,114330456032100,749760805916430
%N A262394 a(n) = (1/n)*Sum_{k=1..n} k*binomial(n,k-1)*binomial(2*n,n-k).
%H A262394 G. C. Greubel, <a href="/A262394/b262394.txt">Table of n, a(n) for n = 1..1000</a>
%F A262394 G.f.: x*B'(x) + B(x) - B'(x)/B(x) - 1, where B(x) is g.f. of A001764.
%F A262394 a(n) = (n+2) * binomial(3*n, n-1) / (3*n). - _Vaclav Kotesovec_, Sep 21 2015
%t A262394 Table[Sum[k Binomial[n, k-1] Binomial[2n, n-k], {k, n}]/n, {n, 30}] (* _Michael De Vlieger_, Sep 21 2015 *)
%o A262394 (Maxima)
%o A262394 a(n):=sum(k*binomial(n,k-1)*binomial(2*n,n-k),k,1,n)/n;
%o A262394 (PARI) a(n)=sum(k=1,n,(k*binomial(n,k-1)*binomial(2*n,n-k))/n) \\ _Anders Hellström_, Sep 21 2015
%o A262394 (Magma) [(n+2)*Binomial(3*n,n)/(3*(2*n+1)): n in [1..30]]; // _G. C. Greubel_, Nov 09 2022
%o A262394 (SageMath) [(n+2)*binomial(3*n,n)/(3*(2*n+1)) for n in range(1,31)] # _G. C. Greubel_, Nov 09 2022
%Y A262394 Cf. A001764.
%K A262394 nonn
%O A262394 1,2
%A A262394 _Vladimir Kruchinin_, Sep 21 2015