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%I #22 Sep 08 2022 08:44:52
%S 1,36,756,12096,163296,1959552,21555072,221709312,2161665792,
%T 20175547392,181579926528,1584697540608,13469929095168,
%U 111904026329088,911218500108288,7289748000866304,57406765506822144,445746649817677824
%N Expansion of 1/(1-6*x)^6.
%H Vincenzo Librandi, <a href="/A036084/b036084.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (36, -540, 4320, -19440, 46656, -46656).
%F a(n) = 6^n*binomial(n+5, 5).
%F G.f.: 1/(1-6*x)^6.
%p seq(binomial(n+5,5)*6^n,n=0..17); # _Zerinvary Lajos_, Jun 16 2008
%t CoefficientList[Series[1/(1-6x)^6,{x,0,30}],x] (* or *) LinearRecurrence[ {36,-540,4320,-19440,46656,-46656},{1,36,756,12096,163296,1959552},30] (* _Harvey P. Dale_, Jul 31 2018 *)
%o (Sage)[lucas_number2(n, 6, 0)*binomial(n,5)/6^5for n in range(5, 23)] # _Zerinvary Lajos_, Mar 13 2009]
%o (Magma) [6^n* Binomial(n+5, 5): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%Y Cf. A001787, A036071.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_
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