A161201 - OEIS

%I #14 Sep 24 2024 11:25:22

%S 1,7,63,231,3003,9009,51051,138567,2909907,7436429,37182145,91265265,

%T 882230895,2103781365,9917826435,23141595015,856239015555,

%U 1964313035685,8948537162565,20251952525805,182267572732245

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

%H G. C. Greubel, <a href="/A161201/b161201.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = (-1)^n*numerator( binomial(-7/2, n) ). - _G. C. Greubel_, Sep 24 2024

%t CoefficientList[Series[(1-x)^(-7/2),{x,0,20}],x]//Numerator (* _Harvey P. Dale_, Jan 14 2020 *)

%t Table[(-1)^n*Numerator[Binomial[-7/2, n]], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2024 *)

%o (Magma)

%o A161201:= func< n | Numerator((n+1)*(2*n+1)*(2*n+3)*(2*n+5)*Catalan(n)/(15*4^n)) >;

%o [A161201(n): n in [0..30]]; // _G. C. Greubel_, Sep 24 2024

%o (SageMath)

%o def A161201(n): return (-1)^n*numerator(binomial(-7/2,n))

%o [A161201(n) for n in range(31)] # _G. C. Greubel_, Sep 24 2024

%Y Cf. A046161 (denominators).

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

%Y 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).

%K easy,nonn,frac,changed

%O 0,2

%A _Johannes W. Meijer_, Jun 08 2009