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 A100096 #18 Jan 16 2025 21:55:26
%S A100096 0,1,1,6,9,36,66,218,449,1332,2946,8196,18954,50688,120576,314586,
%T A100096 761889,1957092,4794426,12194828,30093854,76067256,188595276,
%U A100096 474810276,1180734234,2965094536,7387570516,18521858088,46203981924,115721310552
%N A100096 An inverse Chebyshev transform of the Jacobsthal numbers.
%C A100096 Image of x/(1-x-2*x^2) under the transform g(x)->(1/sqrt(1-4*x^2))*g(x*c(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. This is the inverse of the Chebyshev transform which takes A(x) to ((1-x^2)/(1+x^2))*A(x/(1+x^2)).
%C A100096 Hankel transform is (-1)^n*n. Hankel transform of a(n+1) is A141124. - _Paul Barry_, Jun 05 2008
%H A100096 Vincenzo Librandi, <a href="/A100096/b100096.txt">Table of n, a(n) for n = 0..1000</a>
%F A100096 G.f.: x*sqrt(1-4*x^2)*(3*sqrt(1-4*x^2)+2*x+1)/(2*(4*x^2-1)*(10*x^2+x-2)).
%F A100096 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*A001045(n-2*k).
%F A100096 Conjecture: 2*(-n+1)*a(n) +(n+3)*a(n-1) +18*(n-2)*a(n-2) +4*(-n-2)*a(n-3) +40*(-n+3)*a(n-4)=0. - _R. J. Mathar_, Nov 24 2012
%F A100096 a(n) ~ (5/2)^n / 3. - _Vaclav Kotesovec_, Feb 12 2014
%t A100096 CoefficientList[Series[x*Sqrt[1-4*x^2]*(3*Sqrt[1-4*x^2]+2*x+1)/(2*(4*x^2-1)*(10*x^2+x-2)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 12 2014 *)
%Y A100096 Cf. A100095, A100097.
%K A100096 nonn,easy
%O A100096 0,4
%A A100096 _Paul Barry_, Nov 03 2004