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A331793
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Expansion of ((1 - 5*x)/sqrt(1 - 10*x + 9*x^2) - 1)/(8*x^2).
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2
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1, 10, 87, 740, 6285, 53550, 458115, 3934600, 33913881, 293244050, 2542684463, 22101612780, 192530903461, 1680415209270, 14692052109915, 128653303453200, 1128147127156785, 9905115333850650, 87066787614156807, 766127762539955700, 6747880819438628541
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (2/(n+2)) * A331516(n) = Sum_{k=0..n} 4^k * binomial(n+1,k) * binomial(n+1,k+1).
n * (n+2) * a(n) = (n+1) * (5 * (2*n+1) * a(n-1) - 9 * n * a(n-2)) for n>1.
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MATHEMATICA
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a[n_] := Sum[4^k * Binomial[n + 1, k] * Binomial[n + 1, k + 1], {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, May 05 2021 *)
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PROG
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(PARI) N=20; x='x+O('x^N); Vec(((1-5*x)/sqrt(1-10*x+9*x^2)-1)/(8*x^2))
(PARI) {a(n) = sum(k=0, n, 4^k*binomial(n+1, k)*binomial(n+1, k+1))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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