A020925 Expansion of (1-4*x)^(13/2).

1, -26, 286, -1716, 6006, -12012, 12012, -3432, -858, -572, -572, -728, -1092, -1848, -3432, -6864, -14586, -32604, -76076, -184184, -460460, -1184040, -3121560, -8414640, -23140260, -64792728, -184410072, -532740208, -1560167752, -4626704368, -13880113104

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1694

Formula

a(n) = (-2)^n * Product_{i=0..n-1} (13-2*i) / n! for n>0. - R. J. Mathar, Feb 19 2008

D-finite with recurrence: n*a(n) - 2*(2*n-13)*a(n-1) = 0 for n>0. - Bruno Berselli, Jul 02 2018

a(n) ~ -135135 * 2^(2*n - 7) / (sqrt(Pi) * n^(15/2)). - Vaclav Kotesovec, Jul 02 2018

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(13/2, n).

Sum_{n>=0} 1/a(n) = 960/1001 - 10*Pi/(3^8*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 244659776/234609375 - 12*log(phi)/(5^7*sqrt(5)), where phi is the golden ratio (A001622). (End)

Maple

f := k -> -135135*(2*k)!/((2*k-1)*(2*k-3)*(2*k-5)*(2*k-7)*(2*k-9)*(2*k-11)*(-13+2*k)*(k!)^2):
map(f, [$0..30]); # Robert Israel, Jul 02 2018

Mathematica

CoefficientList[Series[(1-4*x)^(13/2), {x, 0, 50}], x] (* Amiram Eldar, Mar 25 2022 *)

Prog

(PARI) my(x = 'x + O('x^40)); Vec((1-4*x)^(13/2)) \\ Michel Marcus, Jul 02 2018

Crossrefs

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

Sequence in context: A130901 A336732 A227332 * A224331 A125414 A208600

Adjacent sequences: A020922 A020923 A020924 * A020926 A020927 A020928

Keyword

sign

Author

N. J. A. Sloane

Status

approved