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A299501 Expansion of (1 - 6*x + 7*x^2 - 2*x^3 + x^4)^(-1/2). 1
1, 3, 10, 37, 145, 588, 2437, 10251, 43582, 186785, 805585, 3492064, 15200753, 66399763, 290910490, 1277803957, 5625184321, 24811849020, 109631120869, 485153695995, 2149941422590, 9539307910561, 42374000475457, 188421560848512, 838633172823745, 3735857124917763 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See A299500 for a family of related polynomials.
LINKS
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
Sequence in context: A151054 A052893 A052818 * A226434 A151055 A151056
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 15 2018
STATUS
approved

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Last modified June 19 02:16 EDT 2024. Contains 373492 sequences. (Running on oeis4.)