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 A036084 #28 Jul 07 2025 20:03:55
%S A036084 1,36,756,12096,163296,1959552,21555072,221709312,2161665792,
%T A036084 20175547392,181579926528,1584697540608,13469929095168,
%U A036084 111904026329088,911218500108288,7289748000866304,57406765506822144,445746649817677824
%N A036084 Expansion of 1/(1-6*x)^6.
%H A036084 Vincenzo Librandi, <a href="/A036084/b036084.txt">Table of n, a(n) for n = 0..400</a>
%H A036084 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (36, -540, 4320, -19440, 46656, -46656).
%F A036084 a(n) = 6^n*binomial(n+5, 5).
%F A036084 G.f.: 1/(1-6*x)^6.
%F A036084 a(n) = 36*a(n-1) - 540*a(n-2) + 4320*a(n-3) - 19440*a(n-4) + 46656*a(n-5) - 46656*a(n-6). - _Wesley Ivan Hurt_, Jul 07 2025
%p A036084 seq(binomial(n+5,5)*6^n,n=0..17); # _Zerinvary Lajos_, Jun 16 2008
%t A036084 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 A036084 (Sage) [lucas_number2(n, 6, 0)*binomial(n,5)/6^5 for n in range(5, 23)] # _Zerinvary Lajos_, Mar 13 2009
%o A036084 (Magma) [6^n* Binomial(n+5, 5): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%Y A036084 Cf. A001787, A036071.
%K A036084 nonn,easy
%O A036084 0,2
%A A036084 _Wolfdieter Lang_