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 A104497 #18 Jan 18 2025 07:42:55
%S A104497 1,-2,-10,-52,-282,-1596,-9412,-57640,-364922,-2376812,-15852204,
%T A104497 -107821656,-745342500,-5221954776,-36997822536,-264620356944,
%U A104497 -1907962439994,-13852652486220,-101186612941084,-743057485099384,-5482375128919820,-40620301416309128
%N A104497 Expansion of sqrt(1-8x)/sqrt(1-4x).
%C A104497 Convolution of A098579 and A000984.
%C A104497 Hankel transform is (-2)^n*A002315(n).
%F A104497 Moment representation: a(n) = (1/Pi)*Integral_{x = 4..8} (x^n*sqrt((8 - x)*(x - 4))/(x*(4 - x))) dx + sqrt(2)*0^n;
%F A104497 Also a(n) = C(2*n, n) - Sum_{k = 1..n} 2^(k+1)*C(2*k-2, k-1)*C(2*n-2*k, n-k)/k.
%F A104497 From _Peter Bala_, Feb 03 2024: (Start)
%F A104497 a(n) = - 2*A104498(n) for n >= 1.
%F A104497 G.f.: c(-x/(1 - 8*x)) / c(x/(1 - 4*x)), where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the g.f. of the Catalan numbers A000108.
%F A104497 P-recursive: n*a(n) = (12*n - 14)*a(n-1) - 32*(n - 2)*a(n-2) with a(0) = 1 and a(1) = -2. (End)
%Y A104497 Cf. A000108, A104498.
%K A104497 easy,sign
%O A104497 0,2
%A A104497 _Paul Barry_, Mar 11 2005, Mar 07 2008