# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a100099 Showing 1-1 of 1 %I A100099 #16 Aug 30 2024 21:41:23 %S A100099 0,1,2,7,16,46,110,295,720,1870,4612,11782,29224,73984,184102,463687, %T A100099 1156000,2902870,7245020,18161170,45356736,113576596,283765132, %U A100099 710118262,1774619616,4439253196,11095532840,27749232700,69363052600 %N A100099 An inverse Chebyshev transform of x/(1-2x). %C A100099 Image of x/(1-2x) under the transform g(x)->(1/sqrt(1-4x^2)g(xc(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 A100099 Hankel transform is A125905(n-1), the alternating sign version of A001353. - _Paul Barry_, Nov 25 2007 %H A100099 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 %F A100099 G.f.: sqrt(1-4x^2)(sqrt(1-4x^2)+4x-1)/(2(5x-2)(4x^2-1)). %F A100099 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*(2^(n-2*k)-0^(n-2*k))/2. %F A100099 a(n) = Sum_{k=0..n} C(n,floor(k/2))*A001045(n-k). - _Paul Barry_, Nov 25 2007 %F A100099 Conjecture: 2n*a(n) +(-13n+16)*a(n-1) +4(3n-8)*a(n-2) +4(13n-29)*a(n-3) +80(3-n)*a(n-4)=0. - _R. J. Mathar_, Dec 14 2011 %F A100099 a(n) ~ 5^n / 2^(n+1). - _Vaclav Kotesovec_, Feb 01 2014 %t A100099 CoefficientList[Series[Sqrt[1-4*x^2]*(Sqrt[1-4*x^2]+4*x-1)/(2*(5*x-2)*(4*x^2-1)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 01 2014 *) %K A100099 easy,nonn %O A100099 0,3 %A A100099 _Paul Barry_, Nov 04 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE