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