This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A034977 #30 Aug 18 2025 02:24:48
%S A034977 1,8,288,13056,652800,34467840,1884241920,105517547520,6014500208640,
%T A034977 347504456499200,20294260259553280,1195516422562775040,
%U A034977 70933974405391319040,4234212626044897198080,254052757562693831884800,15310912855778348268257280,926310227774590070229565440
%N A034977 Expansion of 1/(1-64*x)^(1/8), related to octo-factorial numbers A045755.
%H A034977 Seiichi Manyama, <a href="/A034977/b034977.txt">Table of n, a(n) for n = 0..500</a>
%H A034977 Armin Straub, Victor H. Moll, and Tewodros 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).
%H A034977 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A034977 a(n) = 8^n*A045755(n)/n!, n >= 1, where A045755(n) = (8*n-7)!^8 = Product_{j=1..n} (8*j-7).
%F A034977 G.f.: (1-64*x)^(-1/8).
%F A034977 D-finite with recurrence: n*a(n) = 8*(8*n-7)*a(n-1). - _R. J. Mathar_, Jan 28 2020
%F A034977 a(n) ~ 2^(6*n) * n^(-7/8) / Gamma(1/8). - _Amiram Eldar_, Aug 18 2025
%t A034977 CoefficientList[Series[1/(1-64x)^(1/8),{x,0,30}],x] (* _Harvey P. Dale_, May 20 2011 *)
%o A034977 (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 A034977 (SageMath) [2^(6*n)*rising_factorial(1/8,n)/factorial(n) for n in range(40)] # _G. C. Greubel_, Oct 21 2022
%Y A034977 Cf. A004993, A034855, A045755, A203142.
%K A034977 easy,nonn
%O A034977 0,2
%A A034977 _Wolfdieter Lang_
%E A034977 a(11) corrected by _Harvey P. Dale_, May 20 2011