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 A134770 #23 Oct 13 2023 14:18:09
%S A134770 1,5,21,77,277,1005,3693,13725,51477,194477,739021,2821725,10816621,
%T A134770 41602397,160466397,620470077,2404321557,9334424877,36300541197,
%U A134770 141381055197,551386115277,2153031497757,8416395854877,32933722910397,128990414732397,505642425751005,1983674131792413
%N A134770 a(n) = 4*A000984(n) - 3.
%C A134770 The second inverse binomial transform of this sequence is A134771, the sequence interleaved with threes: (1, 3, 5, 3, 21, 3, 77, 3, ...).
%H A134770 G. C. Greubel, <a href="/A134770/b134770.txt">Table of n, a(n) for n = 0..1000</a>
%F A134770 From _G. C. Greubel_, Oct 13 2023: (Start)
%F A134770 a(n) = 4*(n+1)*A000108(n) - 3.
%F A134770 G.f.: 4/sqrt(1-4*x) - 3/(1-x).
%F A134770 Sum_{n>=0} a(n)*x^(2*n)/(2*n)! = 4*BesselI(0, 2*x) - cosh(x). (End)
%e A134770 a(2) = 21 = 4*A000984(2) - 3 = 4*6 - 3.
%t A134770 Table[4 Binomial[2n,n]-3,{n,0,30}] (* _Harvey P. Dale_, Dec 01 2022 *)
%o A134770 (PARI) a(n)=4*binomial(2*n, n) - 3; \\ _Michel Marcus_, Jul 02 2020
%o A134770 (Magma) [4*(n+1)*Catalan(n)-3: n in [0..40]]; // _G. C. Greubel_, Oct 13 2023
%o A134770 (SageMath) [4*binomial(2*n,n)-3 for n in range(41)] # _G. C. Greubel_, Oct 13 2023
%Y A134770 Cf. A000108, A000984, A134771.
%K A134770 nonn
%O A134770 0,2
%A A134770 _Gary W. Adamson_, Nov 10 2007
%E A134770 a(10) corrected and offsets aligned by _Georg Fischer_, Jul 01 2020
%E A134770 More terms from _Michel Marcus_, Jul 02 2020