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%I #49 Sep 08 2022 08:45:34
%S 1,18,180,1320,7920,41184,192192,823680,3294720,12446720,44808192,
%T 154791936,515973120,1666990080,5239111680,16066609152,48199827456,
%U 141764198400,409541017600,1163958681600,3259084308480,9001280471040
%N a(n) = binomial(n+8,8) * 2^n.
%C With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly eight (8) u's. See example.
%C Number of 8D hypercubes in an (n+8)-dimensional hypercube. [_Zerinvary Lajos_, Jan 29 2010]
%H Vincenzo Librandi, <a href="/A140325/b140325.txt">Table of n, a(n) for n = 0..400</a>
%H Milan Janjic and Boris Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv:1301.4550 [math.CO], 2013.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18,-144,672,-2016,4032,-5376,4608,-2304,512).
%F a(n) = A038207(n+8,8).
%F G.f.: 1/(1-2*x)^9. - _R. J. Mathar_, Feb 11 2010
%F a(n) = 2*a(n-1) + A054851(n-1). - _Ruskin Harding_, May 12 2013
%F a(n) = Sum_{i=8..n+8} binomial(i,8)*binomial(n+8,i). Example: for n=6, a(6) = 1*3003 + 9*2002 + 45*1001 + 165*364 + 495*91 + 1287*14 + 3003*1 = 192192. - _Bruno Berselli_, Mar 23 2018
%F From _Amiram Eldar_, Jan 07 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1276/105 - 16*log(2).
%F Sum_{n>=0} (-1)^n/a(n) = 34992*log(3/2) - 496548/35. (End)
%e Example: a(1)=18 because we have uuuuuuuuv, uuuuuuuvu, uuuuuuvuu, uuuuuvuuu, uuuuvuuuu, uuuvuuuuu, uuvuuuuuu, uvuuuuuuu, vuuuuuuuu, uuuuuuuuz, uuuuuuuzu, uuuuuuzuu, uuuuuzuuu, uuuuzuuuu, uuuzuuuuu, uuzuuuuuu, uzuuuuuuu and zuuuuuuu.
%p seq(binomial(n+8,8)*2^n,n=0..28);
%t Table[Binomial[n + 8, 8] 2^n, {n, 0, 20}] (* _Zerinvary Lajos_, Jan 29 2010 *)
%o (Magma) [2^n*Binomial(n+8, 8): n in [0..30]]; // _Vincenzo Librandi_, Oct 14 2011
%Y Cf. A038207, A054851.
%K nonn,easy
%O 0,2
%A _Zerinvary Lajos_, Jun 23 2008
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