A161201 Numerators in expansion of (1-x)^(-7/2).

1, 7, 63, 231, 3003, 9009, 51051, 138567, 2909907, 7436429, 37182145, 91265265, 882230895, 2103781365, 9917826435, 23141595015, 856239015555, 1964313035685, 8948537162565, 20251952525805, 182267572732245

Offset: 0

Author

Johannes W. Meijer, Jun 08 2009

Keywords

• easy
• nonn
• 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) ): A161202 (p=5), A161200 (p=3), A002596 (p=1), A001790 (p=-1), A001803 (p=-3), A161199 (p=-5), this sequence (p=-7).

Programs

Magma

A161201:= func< n | Numerator((n+1)*(2*n+1)*(2*n+3)*(2*n+5)*Catalan(n)/(15*4^n)) >;
[A161201(n): n in [0..30]]; // G. C. Greubel, Sep 24 2024

Mathematica

CoefficientList[Series[(1-x)^(-7/2),{x,0,20}],x]//Numerator (* Harvey P. Dale, Jan 14 2020 *)
Table[(-1)^n*Numerator[Binomial[-7/2, n]], {n, 0, 30}] (* G. C. Greubel, Sep 24 2024 *)

SageMath

def A161201(n): return (-1)^n*numerator(binomial(-7/2,n))
[A161201(n) for n in range(31)] # G. C. Greubel, Sep 24 2024

Formula

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

a(n) = (-1)^n*numerator( binomial(-7/2, n) ). - G. C. Greubel, Sep 24 2024