A034977 - OEIS

%I #21 Oct 21 2022 06:58:40

%S 1,8,288,13056,652800,34467840,1884241920,105517547520,6014500208640,

%T 347504456499200,20294260259553280,1195516422562775040,

%U 70933974405391319040,4234212626044897198080,254052757562693831884800

%N Expansion of 1/(1-64*x)^(1/8), related to octo-factorial numbers A045755.

%H Seiichi Manyama, <a href="/A034977/b034977.txt">Table of n, a(n) for n = 0..500</a>

%H A. Straub, V. H. Moll, and T. Amdeberhan, <a href="http://dx.doi.org/10.4064/aa140-1-2">The p-adic valuation of k-central binomial coefficients</a>, Acta Arith. 140 (1) (2009) 31-41, eq (1.10).

%F a(n) = 8^n*A045755(n)/n!, n >= 1, A045755(n)=(8*n-7)!^8 := Product_{j=1..n} (8*j-7).

%F G.f.: (1-64*x)^(-1/8).

%F D-finite with recurrence: n*a(n) = 8*(8*n-7)*a(n-1). - _R. J. Mathar_, Jan 28 2020

%t CoefficientList[Series[1/(1-64x)^(1/8),{x,0,30}],x] (* _Harvey P. Dale_, May 20 2011 *)

%o (Magma) [n le 1 select 8^(n-1) else 8*(8*n-15)*Self(n-1)/(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 21 2022

%o (SageMath) [2^(6*n)*rising_factorial(1/8,n)/factorial(n) for n in range(40)] # _G. C. Greubel_, Oct 21 2022

%Y Cf. A004993, A034855, A045755.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_

%E a(11) corrected by _Harvey P. Dale_, May 20 2011