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A291699
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a(n) = n^n*(2*n)!/(n!*(n + 1)!).
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5
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1, 1, 8, 135, 3584, 131250, 6158592, 353299947, 23991418880, 1883638417518, 167960000000000, 16772331868538246, 1854655886442627072, 225005916687384753700, 29718395534545380311040, 4245313393689422607421875, 652233889532678001886494720, 107247390031799133661006687830
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^n] 2/(1 + sqrt(1 - 4*n*x)).
a(n) = [x^n] 1/(1 - n*x/(1 - n*x/(1 - n*x/(1 - n*x/(1 - n*x/(1 - ...)))))), a continued fraction.
a(n) = n! * [x^n] (BesselI(0,2*n*x) - BesselI(1,2*n*x))*exp(2*n*x).
a(n) = n^n*binomial(2*n,n)/(n + 1).
a(n) ~ 4^n*n^(n-3/2)/sqrt(Pi).
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MAPLE
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MATHEMATICA
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Join[{1}, Table[n^n (2 n)!/(n! (n + 1)!), {n, 1, 17}]]
Table[SeriesCoefficient[2/(1 + Sqrt[1 - 4 n x]), {x, 0, n}], {n, 0, 17}]
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 17}]
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PROG
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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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