A020933 Expansion of (1-4*x)^(21/2).

1, -42, 798, -9044, 67830, -352716, 1293292, -3325608, 5819814, -6466460, 3879876, -705432, -117572, -54264, -38760, -36176, -40698, -52668, -76076, -120120, -204204, -369512, -705432, -1410864, -2939300, -6348888, -14162904, -32522224, -76659528, -185040240

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Crossrefs

Cf. A001622, A002420, A002421, A002422, A002423, A002424, A020923, A020925, A020927, A020929, A020931.

Programs

Mathematica

CoefficientList[Series[Surd[(1-4x)^21,2],{x,0,30}],x] (* Harvey P. Dale, Feb 25 2020 *)

Formula

D-finite with recurrence: n*a(n) +2*(-2*n+23)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(21/2, n).

Sum_{n>=0} 1/a(n) = 406240/415701 - 46*Pi/(3^13*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 728323714975904/710426513671875 - 92*log(phi)/(5^12*sqrt(5)), where phi is the golden ratio (A001622). (End)