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%I #15 Jan 30 2020 21:29:18
%S 1,3,13,67,349,1875,10285,57123,320317,1809587,10283149,58714627,
%T 336579101,1935878419,11166265837,64566715363,374148669949,
%U 2172215118963,12632572359757,73575490895043,429102329027293,2505638311638739,14647279574704045,85710562407867555
%N Expansion of (1 - 6*x + x^2 - 8*x^3 + 16*x^4)^(-1/2).
%C See A299499 for a family of related polynomials.
%F a(n) = Sum_{k=0..n} 2^(n-k)*binomial(n,k)*hypergeom([-k, k-n, k-n], [1, -n], 2).
%F D-finite with recurrence: (16*n-32)*a(n-4) + (-8*n+12)*a(n-3) + (n-1)*a(n-2) + (-6*n+3)*a(n-1) + n*a(n) = 0.
%p a := n -> add(2^(n-k)*binomial(n,k)*hypergeom([-k,k-n,k-n],[1,-n],2), k=0..n): seq(simplify(a(n)), n=0..23);
%t CoefficientList[Series[(1 - 6 x + x^2 - 8 x^3 + 16 x^4)^(-1/2), {x, 0, 23}], x]
%Y Cf. A299499, A299502.
%K nonn
%O 0,2
%A _Peter Luschny_, Feb 15 2018
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