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Numerators in expansion of (1-x)^(5/2).
8

%I #17 Sep 24 2024 14:15:07

%S 1,-5,15,-5,-5,-3,-5,-5,-45,-55,-143,-195,-1105,-1615,-4845,-7429,

%T -185725,-294975,-950475,-1550775,-10235115,-17058525,-57378675,

%U -97294275,-1329688425,-2287064091,-7916760315,-13781027215

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

%H G. C. Greubel, <a href="/A161202/b161202.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = (-1)^n*numerator( binomial(5/2, n) ). - _G. C. Greubel_, Sep 24 2024

%t Numerator[CoefficientList[Series[(1-x)^(5/2),{x,0,30}],x]] (* _Harvey P. Dale_, Aug 22 2011 *)

%t Table[(-1)^n*Numerator[Binomial[5/2, n]], {n,0,30}] (* _G. C. Greubel_, Sep 24 2024 *)

%o (Magma)

%o A161202:= func< n | -Numerator(15*(n+1)*Catalan(n)/(4^n*(2*n-1)*(2*n-3)*(2*n-5))) >;

%o [A161202(n): n in [0..30]]; // _G. C. Greubel_, Sep 24 2024

%o (SageMath)

%o def A161202(n): return (-1)^n*numerator(binomial(5/2,n))

%o [A161202(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) ): this sequence (p=5), A161200 (p=3), A002596 (p=1), A001790 (p=-1), A001803 (p=-3), A161199 (p=-5), A161201 (p=-7).

%K easy,sign,frac

%O 0,2

%A _Johannes W. Meijer_, Jun 08 2009