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 A099045 #15 Sep 08 2022 08:45:15
%S A099045 1,2,24,320,4480,64512,946176,14057472,210862080,3186360320,
%T A099045 48432676864,739699064832,11342052327424,174493112729600,
%U A099045 2692179453542400,41639042214789120,645405154329231360,10022762396642181120,155909637281100595200
%N A099045 a(n) = (3*0^n + 4^n*binomial(2*n,n))/4.
%C A099045 (1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.
%H A099045 Vincenzo Librandi, <a href="/A099045/b099045.txt">Table of n, a(n) for n = 0..800</a>
%F A099045 G.f.: (1+3*sqrt(1-16*x))/(4*sqrt(1-16*x)).
%F A099045 n*a(n) +8*(-2*n+1)*a(n-1)=0. - _R. J. Mathar_, Nov 24 2012
%F A099045 E.g.f.: (3 + exp(8*x) * BesselI(0,8*x)) / 4. - _Ilya Gutkovskiy_, Nov 17 2021
%t A099045 Join[{1}, Table[4^(n-1)*Binomial[2*n,n], {n,1,30}]] (* _G. C. Greubel_, Dec 31 2017 *)
%o A099045 (Magma) [(3*0^n + 4^n*Binomial(2*n, n))/4: n in [ 0..20]]; // _Vincenzo Librandi_, Nov 24 2012
%o A099045 (PARI) for(n=0,30, print1((3*0^n + 4^n*binomial(2*n,n))/4, ", ")) \\ _G. C. Greubel_, Dec 31 2017
%Y A099045 Cf. A069723, A088218, A099044, A099046.
%K A099045 easy,nonn
%O A099045 0,2
%A A099045 _Paul Barry_, Sep 24 2004