A161199 Numerators in expansion of (1-x)^(-5/2).

1, 5, 35, 105, 1155, 3003, 15015, 36465, 692835, 1616615, 7436429, 16900975, 152108775, 339319575, 1502700975, 3305942145, 115707975075, 251835004575, 1091285019825, 2354878200675, 20251952525805, 43397041126725, 185423721177825, 395033145117975

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

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

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}]] (* Harvey P. Dale, Oct 15 2011 *)

Prog

(Magma)
A161199:= func< n | Numerator( Binomial(n+3, 3)*Catalan(n+2)/2^(2*n+1) ) >;
[A161199(n): n in [0..30]]; // G. C. Greubel, Sep 24 2024
(SageMath)
def A161199(n): return numerator((-1)^n*binomial(-5/2, n))
[A161199(n) for n in range(31)] # G. C. Greubel, Sep 24 2024

Crossrefs

Cf. A161198 (triangle for (1-x)^((-1-2*n)/2) for all values of n).

Cf. A046161 (denominators for (1-x)^(-5/2)).

Numerators of [x^n]( (1-x)^(p/2) ): A161202 (p=5), A161200 (p=3), A002596 (p=1), A001790 (p=-1), A001803 (p=-3), this sequence (p=-5), A161201 (p=-7).

Sequence in context: A369812 A090294 A162540 * A111877 A179337 A053126

Adjacent sequences: A161196 A161197 A161198 * A161200 A161201 A161202

Keyword

easy,nonn,frac

Author

Johannes W. Meijer, Jun 08 2009

Status

approved