A020923 Expansion of (1-4*x)^(11/2).

1, -22, 198, -924, 2310, -2772, 924, 264, 198, 220, 308, 504, 924, 1848, 3960, 8976, 21318, 52668, 134596, 354200, 956340, 2641320, 7443720, 21360240, 62300700, 184410072, 553230216, 1680180656, 5160554872, 16015515120, 50181947376, 158639704608, 505664058438

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = (10395/64)*4^n*Gamma(-11/2+n)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015

D-finite with recurrence: n*a(n) +2*(-2*n+13)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(11/2, n).

Sum_{n>=0} 1/a(n) = 1124/1155 + 26*Pi/(3^8*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 56972276/54140625 - 52*log(phi)/(5^7*sqrt(5)), where phi is the golden ratio (A001622). (End)

Maple

A002423 := n -> (10395/64)*4^n*GAMMA(-11/2+n)/(sqrt(Pi)*GAMMA(1+n)):
seq(A002423(n), n=0..28); # Peter Luschny, Dec 14 2015

Mathematica

CoefficientList[Series[(1 - 4*x)^(11/2), {x, 0, 50}], x] (* G. C. Greubel, Feb 15 2017 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1-4*x)^(11/2)) \\ G. C. Greubel, Feb 15 2017

Crossrefs

Cf. A001622, A002420, A002421, A002422, A002423, A002424.

Sequence in context: A107959 A200936 A110690 * A254470 A230896 A031202

Adjacent sequences: A020920 A020921 A020922 * A020924 A020925 A020926

Keyword

sign

Author

N. J. A. Sloane

Status

approved