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A299506
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a(n) = hypergeom([-n, n - 1/2], [1], -4).
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2
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1, 3, 43, 661, 10515, 171097, 2828101, 47284251, 797456947, 13540982665, 231188344401, 3964874384863, 68252711769373, 1178662654873191, 20409993947488075, 354260920943874245, 6161735337225790035, 107368528677807960185, 1873946997372948997345, 32754419073618998202975
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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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Recurrence: n*(2*n - 3)*(4*n - 7)*a(n) = 9*(4*n - 5)*(4*n^2 - 10*n + 5)*a(n-1) - (n-1)*(2*n - 5)*(4*n - 3)*a(n-2).
a(n) ~ 2^(-3/2) * sqrt(5) * phi^(6*n - 3/2) / sqrt(Pi*n), where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. (End)
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MATHEMATICA
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a[n_] := Hypergeometric2F1[-n, n - 1/2, 1, -4]; Table[a[n], {n, 0, 19}]
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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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