OFFSET
0,2
COMMENTS
See A299500 for a family of related polynomials.
FORMULA
a(n) = Sum_{k=0..n} 2^(n-k)*binomial(n, k)*hypergeom([-k, k-n, k-n], [1, -n], 1/2).
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.
A249946(n) = a(n) - 2*a(n-1) + a(n-2) for n >= 2.
MAPLE
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);
MATHEMATICA
CoefficientList[Series[(1 - 6 x + 7 x^2 - 2 x^3 + x^4 )^(-1/2), {x, 0, 25}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 15 2018
STATUS
approved