A301271 - OEIS

%I #68 Jan 30 2020 21:29:18

%S 1,-2,-14,-140,-1610,-19964,-259532,-3485144,-47920730,-670890220,

%T -9526641124,-136837208872,-1984139528644,-28998962341720,

%U -426699017313880,-6315145456245424,-93937788661650682,-1403541077650545484,-21053116164758182260,-316904801216886322440

%N Expansion of (1-16*x)^(1/8).

%H Seiichi Manyama, <a href="/A301271/b301271.txt">Table of n, a(n) for n = 0..833</a>

%F a(n) = 2^n/n! * Product_{k=0..n-1} (8*k - 1) for n > 0.

%F a(n) = -sqrt(2-sqrt(2)) * Gamma(1/8) * Gamma(n-1/8) * 16^(n-1) / (Pi*Gamma(n+1)). - _Vaclav Kotesovec_, Jun 16 2018

%F a(n) ~ -2^(4*n-3) / (Gamma(7/8) * n^(9/8)). - _Vaclav Kotesovec_, Jun 16 2018

%F D-finite with recurrence: n*a(n) +2*(-8*n+9)*a(n-1)=0. - _R. J. Mathar_, Jan 20 2020

%F a(n) = -2*A097184(n-1). - _R. J. Mathar_, Jan 20 2020

%o (PARI) N=20; x='x+O('x^N); Vec((1-16*x)^(1/8))

%Y Cf. A003557, A007947.

%Y (1-b*x)^(1/A003557(b)): A002420 (b=4), A004984 (b=8), A004990 (b=9), (-1)^n * A108735 (b=12), this sequence (b=16), (-1)^n * A108733 (b=18), A049393 (b=25), A004996 (b=36), A303007 (b=240), A303055 (b=504), A305886 (b=1728).

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 15 2018