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 A239488 #26 Jan 30 2020 21:29:17 %S A239488 6,30,186,1290,9582,74550,599730,4948050,41638614,356007630, %T A239488 3083837802,27006251610,238704231102,2126733078630,19079571337314, %U A239488 172209370246050,1562686251141030,14248144422407550,130467052593799962 %N A239488 Expansion of 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3. %F A239488 a(n) = sum(i = 0..n+1, 2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1))/n. %F A239488 a(n) = T(2*n,n-1)/n where T(n,k) is triangle A116412. %F A239488 D-finite with recurrence: (n+1)*a(n) +5*(-2*n+1)*a(n-1) +(n-2)*a(n-2)=0. a(n) = 2*A103210(n). - _R. J. Mathar_, May 23 2014 %p A239488 ogf := 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3; %p A239488 series(ogf, x=0, 20): seq(coeff(%,x,n), n=0..19); # _Peter Luschny_, Mar 21 2014 %o A239488 (Maxima) a(n):=sum(2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1),i,0,n+1)/n; %Y A239488 Cf. A103210. %K A239488 nonn %O A239488 1,1 %A A239488 _Vladimir Kruchinin_, Mar 20 2014