A020931 Expansion of (1-4*x)^(19/2).

1, -38, 646, -6460, 41990, -184756, 554268, -1108536, 1385670, -923780, 184756, 33592, 16796, 12920, 12920, 15504, 21318, 32604, 54340, 97240, 184756, 369512, 772616, 1679600, 3779100, 8767512, 20907144, 51106352, 127765880, 326023280, 847660528, 2242198816

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Crossrefs

Cf. A001622, A002420, A002421, A002422, A002423, A002424, A020923, A020925, A020927, A020929.

Programs

Mathematica

CoefficientList[Series[(1-4x)^(19/2),{x,0,30}],x] (* Harvey P. Dale, Jul 03 2013 *)

Formula

D-finite with recurrence: n*a(n) +2*(-2*n+21)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(19/2, n).

Sum_{n>=0} 1/a(n) = 45052/46189 + 14*Pi/(3^11*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 6955761045148/6765966796875 - 84*log(phi)/(5^11*sqrt(5)), where phi is the golden ratio (A001622). (End)