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A161199
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Numerators in expansion of (1-x)^(-5/2)
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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = numer(((3+8*n+4*n^2)/3)*binomial(2*n,n)/(4^n))
a(n) = denominator( (3/2)*integral(x^n*sqrt(1-x),x=0..1) ), where the integral is sqrt(Pi)*n!/Gamma(n+5/2) = n!/( (n+3/2)*(n+1/2)*(n-1/2)*..*(1/2)).- Roland Groux, Feb 23 2011
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MATHEMATICA
| 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}]] (* From Harvey P. Dale, Oct 15 2011 *)
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CROSSREFS
| Cf. A001790 [(1-x)^(-1/2)], A001803 [(1-x)^(-3/2)] and A161201 [(1-x)^(-7/2)].
Cf. A161200 Numerators in expansion of (1-x)^(3/2).
A161198 triangle related to the series expansions of (1-x)^((-1-2*n)/2) for all values of n.
A046161 gives the denominators of the series expansions of (1-x)^(-5/2).
Sequence in context: A153785 A090294 A162540 * A111877 A179337 A053126
Adjacent sequences: A161196 A161197 A161198 * A161200 A161201 A161202
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KEYWORD
| easy,nonn
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AUTHOR
| Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009
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