A020929 Expansion of (1-4*x)^(17/2).

1, -34, 510, -4420, 24310, -87516, 204204, -291720, 218790, -48620, -9724, -5304, -4420, -4760, -6120, -8976, -14586, -25740, -48620, -97240, -204204, -447304, -1016600, -2386800, -5768100, -14304888, -36312408, -94143280, -248807240, -669205680, -1829162192

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

D-finite with recurrence: n*a(n) +2*(-2*n+19)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(17/2, n).

Sum_{n>=0} 1/a(n) = 49600/51051 - 38*Pi/(3^11*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 1542987607648/1495634765625 - 76*log(phi)/(5^10*sqrt(5)), where phi is the golden ratio (A001622). (End)

Mathematica

CoefficientList[Series[(1 - 4 x)^(17/2), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 18 2020 *)

Crossrefs

Cf. A001622, A002420, A002421, A002422, A002423, A002424, A020923, A020925, A020927.

Sequence in context: A303104 A066291 A228682 * A160279 A230332 A232320

Adjacent sequences: A020926 A020927 A020928 * A020930 A020931 A020932

Keyword

sign

Author

N. J. A. Sloane

Status

approved