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%I #25 Sep 08 2022 08:45:00
%S 1,64,2304,61440,1351680,25952256,449839104,7197425664,107961384960,
%T 1535450808320,20882130993152,273366078455808,3462636993773568,
%U 42617070692597760,511404848311173120,6000483553517764608,69005560865454292992,779356922715719073792
%N Expansion of 1/(1-8*x)^8.
%C With a different offset, number of n-permutations (n>=7) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly 7 u's. - _Zerinvary Lajos_, Feb 11 2010
%H Vincenzo Librandi, <a href="/A053107/b053107.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (64, -1792, 28672, -286720, 1835008, -7340032, 16777216, -16777216).
%F a(n) = 8^n*binomial(n+7, 7).
%F G.f.: 1/(1-8*x)^8.
%t Table[Binomial[n + 7, 7]*8^n, {n, 0, 20}] (* _Zerinvary Lajos_, Feb 11 2010 *)
%t CoefficientList[Series[1/(1-8x)^8,{x,0,20}],x] (* or *) LinearRecurrence[ {64,-1792,28672,-286720,1835008,-7340032,16777216,-16777216},{1,64,2304,61440,1351680,25952256,449839104,7197425664},20] (* _Harvey P. Dale_, Jul 19 2018 *)
%o (Sage) [lucas_number2(n, 8, 0)*binomial(n,7)/8^7 for n in range(7, 22)] # _Zerinvary Lajos_, Mar 13 2009
%o (Magma) [8^n* Binomial(n+7, 7): n in [0..20]]; // _Vincenzo Librandi_, Oct 16 2011
%o (PARI) vector(30, n, n--; 8^n*binomial(n+7,7)) \\ _G. C. Greubel_, Aug 16 2018
%Y Cf. A036226.
%Y Cf. A081138, A140802, A175210, A140406, A053107, A141054, A173155. - _Zerinvary Lajos_, Feb 11 2010
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
%E More terms from _Harvey P. Dale_, Jul 19 2018
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