A161202 Numerators in expansion of (1-x)^(5/2).

1, -5, 15, -5, -5, -3, -5, -5, -45, -55, -143, -195, -1105, -1615, -4845, -7429, -185725, -294975, -950475, -1550775, -10235115, -17058525, -57378675, -97294275, -1329688425, -2287064091, -7916760315, -13781027215

Offset: 0

Author

Johannes W. Meijer, Jun 08 2009

Keywords

• easy
• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A046161 (denominators).

Cf. A161198 (triangle of coefficients of (1-x)^((-1-2*n)/2)).

Numerators of [x^n]( (1-x)^(p/2) ): this sequence (p=5), A161200 (p=3), A002596 (p=1), A001790 (p=-1), A001803 (p=-3), A161199 (p=-5), A161201 (p=-7).

Programs

Magma

A161202:= func< n | -Numerator(15*(n+1)*Catalan(n)/(4^n*(2*n-1)*(2*n-3)*(2*n-5))) >;
[A161202(n): n in [0..30]]; // G. C. Greubel, Sep 24 2024

Mathematica

Numerator[CoefficientList[Series[(1-x)^(5/2),{x,0,30}],x]] (* Harvey P. Dale, Aug 22 2011 *)
Table[(-1)^n*Numerator[Binomial[5/2, n]], {n,0,30}] (* G. C. Greubel, Sep 24 2024 *)

SageMath

def A161202(n): return (-1)^n*numerator(binomial(5/2,n))
[A161202(n) for n in range(31)] # G. C. Greubel, Sep 24 2024

Formula

a(n) = numerator( (15/(15-46*n+36*n^2-8*n^3))*binomial(2*n,n)/(4^n) ).

a(n) = (-1)^n*numerator( binomial(5/2, n) ). - G. C. Greubel, Sep 24 2024