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A161199
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Numerators in expansion of (1-x)^(-5/2).
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8
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1, 5, 35, 105, 1155, 3003, 15015, 36465, 692835, 1616615, 7436429, 16900975, 152108775, 339319575, 1502700975, 3305942145, 115707975075, 251835004575, 1091285019825, 2354878200675, 20251952525805, 43397041126725, 185423721177825, 395033145117975
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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) = numerator(((3 + 8*n + 4*n^2)/3)*binomial(2*n,n)/(4^n)).
a(n) = denominator((3/2)*Integral_{x=0..1} x^n*sqrt(1-x) dx), where the integral is sqrt(Pi)*n!/Gamma(n+5/2) = n!/( (n+3/2)*(n+1/2)*(n-1/2)*...*(1/2)). - Groux Roland, Feb 23 2011
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MATHEMATICA
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Numerator[CoefficientList[Series[(1-x)^(-5/2), {x, 0, 30}], x]] (* or *) Numerator[Table[(4n^2+8n+3)/3 Binomial[2n, n]/4^n, {n, 0, 30}]] (* Harvey P. Dale, Oct 15 2011 *)
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CROSSREFS
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Cf. A161198 (triangle for (1-x)^((-1-2*n)/2) for all values of n).
Cf. A046161 (denominators for (1-x)^(-5/2)).
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KEYWORD
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easy,nonn,frac
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AUTHOR
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STATUS
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approved
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