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A299443
Expansion of (x^4 + 2*x^3 + 7*x^2 - 6*x + 1)^(-1/2).
3
1, 3, 10, 35, 127, 474, 1807, 6999, 27436, 108541, 432493, 1733174, 6977777, 28200413, 114338320, 464857475, 1894420045, 7736238420, 31649963275, 129693294945, 532216500532, 2186868151211, 8996351889535, 37048736568870, 152722557174139, 630116066189691
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2).
D-finite with recurrence: a(n) = ((2-n)*a(n-4)+(3-2*n)*a(n-3)+(7-7*n)*a(n-2)+(6*n-3)*a(n-1))/n for n >= 4.
EXAMPLE
From the first formula follows that a(n) = p_{n}(1) of the polynomials p_{n}(x):
[0] 1
[1] 3
[2] 9 + x
[3] 27 + 8*x
[4] 81 + 45*x + x^2
[5] 243 + 216*x + 15*x^2
[6] 729 + 945*x + 132*x^2 + x^3
[7] 2187 + 3888*x + 900*x^2 + 24*x^3
...
MAPLE
ogf := (x^4 + 2*x^3 + 7*x^2 - 6*x + 1)^(-1/2):
series(ogf, x, 27): seq(coeff(%, x, n), n=0..25);
MATHEMATICA
CoefficientList[ Series[1/Sqrt[x^4 + 2 x^3 + 7 x^2 - 6 x + 1], {x, 0, 25}], x] (* Robert G. Wilson v, Feb 11 2018 *)
CROSSREFS
Cf. A299444.
Sequence in context: A114196 A346739 A078789 * A128736 A303730 A149037
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 10 2018
STATUS
approved