A299502 Expansion of (1 - 6*x + x^2 + 8*x^3 + 16*x^4)^(-1/2).

1, 3, 13, 59, 277, 1347, 6685, 33675, 171493, 880531, 4550125, 23633627, 123272117, 645247715, 3387538621, 17830213931, 94058445445, 497152260915, 2632288649869, 13958805204603, 74124967884373, 394115410904195, 2097849420888925, 11178238250228427

Offset: 0

Author

Peter Luschny, Feb 15 2018

Keywords

• nonn

Comments

See A299500 for a family of related polynomials.

Crossrefs

Cf. A298611, A299500.

Programs

Maple

a := n -> add(2^k*binomial(n,k)*hypergeom([-k,k-n,k-n], [1,-n], 2), k=0..n):
seq(simplify(a(n)), n=0..28);

Mathematica

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

Formula

a(n) = Sum_{k=0..n} 2^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) + (3-6*n)*a(n-1) + n*a(n) = 0.