A298611 Expansion of (1 - 6*x + x^2 - 8*x^3 + 16*x^4)^(-1/2).

1, 3, 13, 67, 349, 1875, 10285, 57123, 320317, 1809587, 10283149, 58714627, 336579101, 1935878419, 11166265837, 64566715363, 374148669949, 2172215118963, 12632572359757, 73575490895043, 429102329027293, 2505638311638739, 14647279574704045, 85710562407867555

Offset: 0

Author

Peter Luschny, Feb 15 2018

Keywords

• nonn

Comments

See A299499 for a family of related polynomials.

Crossrefs

Cf. A299499, A299502.

Programs

Maple

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);

Mathematica

CoefficientList[Series[(1 - 6 x + x^2 - 8 x^3 + 16 x^4)^(-1/2), {x, 0, 23}], x]

Formula

a(n) = Sum_{k=0..n} 2^(n-k)*binomial(n,k)*hypergeom([-k, k-n, k-n], [1, -n], 2).

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.