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 A134763 #11 May 28 2024 18:28:19
%S A134763 1,2,4,2,16,2,58,2,208,2,754,2,2770,2,10294,2,38608,2,145858,2,554266,
%T A134763 2,2116294,2,8112466,2,31201798,2,120349798,2,465352558,2,1803241168,
%U A134763 2,7000818658,2,27225405898,2,106035791398,2,413539586458,2,1614773623318,2,6312296891158,2
%N A134763 a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).
%C A134763 Second inverse binomial transform of A134762.
%C A134763 A134762 interpolated with two's.
%C A134763 Former name: A000718^(-2) * A134762. - _G. C. Greubel_, May 28 2024
%H A134763 G. C. Greubel, <a href="/A134763/b134763.txt">Table of n, a(n) for n = 0..1000</a>
%F A134763 From _G. C. Greubel_, May 28 2024: (Start)
%F A134763 a(n) = (1/2)*( (1+(-1)^n)*A134762(n/2) + 2*(1-(-1)^n) ).
%F A134763 a(n) = (3/2)*(1+(-1)^n)*A001405(n) - 2*(-1)^n.
%F A134763 G.f.: 3/sqrt(1-4*x^2) - 2/(1+x).
%F A134763 E.g.f.: 3*BesselI(0, 2*x) - 2*exp(-x). (End)
%e A134763 First few terms of the sequence are: (1, 2, 4, 2, 16, 2, 58, ...), interpolating two's in the sequence A134762: (1, 4, 16, 58, ...).
%t A134763 Table[(3/2)*(1+(-1)^n)*Binomial[n,n/2] -2*(-1)^n, {n,0,40}] (* _G. C. Greubel_, May 28 2024 *)
%o A134763 (Magma) [3*((n+1) mod 2)*Binomial(n, Floor(n/2)) - 2*(-1)^n : n in [0..40]]; // _G. C. Greubel_, May 28 2024
%o A134763 (SageMath) [3*((n+1)%2)*binomial(n, n//2) - 2*(-1)^n for n in range(41)] # _G. C. Greubel_, May 28 2024
%Y A134763 Cf. A000718, A000984, A001405, A134758, A134759, A134760, A134761, A134762, A134770, A134771.
%K A134763 nonn
%O A134763 0,2
%A A134763 _Gary W. Adamson_, Nov 09 2007
%E A134763 Name change and terms a(14) onward added by _G. C. Greubel_, May 28 2024