A020927 - OEIS

%I #21 Mar 25 2022 09:14:12

%S 1,-30,390,-2860,12870,-36036,60060,-51480,12870,2860,1716,1560,1820,

%T 2520,3960,6864,12870,25740,54340,120120,276276,657800,1614600,

%U 4071600,10518300,27768312,74760840,204900080,570793080,1613966640,4626704368,13432367520

%N Expansion of (1-4*x)^(15/2).

%F D-finite with recurrence: n*a(n) +2*(-2*n+17)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020

%F From _Amiram Eldar_, Mar 25 2022: (Start)

%F a(n) = (-4)^n*binomial(15/2, n).

%F Sum_{n>=0} 1/a(n) = 972/1001 + 34*Pi/(3^10*sqrt(3)).

%F Sum_{n>=0} (-1)^n/a(n) = 18235778692/17595703125 - 68*log(phi)/(5^9*sqrt(5)), where phi is the golden ratio (A001622). (End)

%t CoefficientList[Series[(1-4x)^(15/2),{x,0,30}],x] (* _Harvey P. Dale_, Oct 03 2012 *)

%Y Cf. A001622, A002420, A002421, A002422, A002423, A002424, A020923, A020925, A020929.

%K sign

%O 0,2

%A _N. J. A. Sloane_