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A020931
Expansion of (1-4*x)^(19/2).
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
0,2
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)
MATHEMATICA
CoefficientList[Series[(1-4x)^(19/2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 03 2013 *)
KEYWORD
sign
STATUS
approved