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%I #19 Mar 25 2022 09:13:49
%S 1,-22,198,-924,2310,-2772,924,264,198,220,308,504,924,1848,3960,8976,
%T 21318,52668,134596,354200,956340,2641320,7443720,21360240,62300700,
%U 184410072,553230216,1680180656,5160554872,16015515120,50181947376,158639704608,505664058438
%N Expansion of (1-4*x)^(11/2).
%H G. C. Greubel, <a href="/A020923/b020923.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = (10395/64)*4^n*Gamma(-11/2+n)/(sqrt(Pi)*Gamma(1+n)). - _Peter Luschny_, Dec 14 2015
%F D-finite with recurrence: n*a(n) +2*(-2*n+13)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020
%F From _Amiram Eldar_, Mar 25 2022: (Start)
%F a(n) = (-4)^n*binomial(11/2, n).
%F Sum_{n>=0} 1/a(n) = 1124/1155 + 26*Pi/(3^8*sqrt(3)).
%F Sum_{n>=0} (-1)^n/a(n) = 56972276/54140625 - 52*log(phi)/(5^7*sqrt(5)), where phi is the golden ratio (A001622). (End)
%p A002423 := n -> (10395/64)*4^n*GAMMA(-11/2+n)/(sqrt(Pi)*GAMMA(1+n)):
%p seq(A002423(n),n=0..28); # _Peter Luschny_, Dec 14 2015
%t CoefficientList[Series[(1 - 4*x)^(11/2), {x,0,50}], x] (* _G. C. Greubel_, Feb 15 2017 *)
%o (PARI) my(x='x+O('x^50)); Vec((1-4*x)^(11/2)) \\ _G. C. Greubel_, Feb 15 2017
%Y Cf. A001622, A002420, A002421, A002422, A002423, A002424.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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