Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jan 30 2020 21:29:18
%S 1,3,10,37,145,588,2437,10251,43582,186785,805585,3492064,15200753,
%T 66399763,290910490,1277803957,5625184321,24811849020,109631120869,
%U 485153695995,2149941422590,9539307910561,42374000475457,188421560848512,838633172823745,3735857124917763
%N Expansion of (1 - 6*x + 7*x^2 - 2*x^3 + x^4)^(-1/2).
%C See A299500 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], 1/2).
%F D-finite with recurrence: (-2+n)*a(-4+n) + (-2*n+3)*a(n-3) + (7*n-7)*a(-2+n) + (-6*n+3)*a(-1+n) + n*a(n) = 0.
%F A249946(n) = a(n) - 2*a(n-1) + a(n-2) for n >= 2.
%p a := n -> add(2^(n-k)*binomial(n, k)*hypergeom([-k, k-n, k-n], [1, -n], 1/2), k=0..n): seq(simplify(a(n)), n=0..25);
%t CoefficientList[Series[(1 - 6 x + 7 x^2 - 2 x^3 + x^4 )^(-1/2), {x, 0, 25}], x]
%Y Cf. A249946, A299500.
%K nonn
%O 0,2
%A _Peter Luschny_, Feb 15 2018