cp's OEIS Frontend

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.

A086603 a(n) = n^3*3^(n-1).

This page as a plain text file.
%I A086603 #24 Sep 08 2022 08:45:11
%S A086603 0,1,24,243,1728,10125,52488,250047,1119744,4782969,19683000,78594219,
%T A086603 306110016,1167575877,4374822312,16142520375,58773123072,211488540273,
%U A086603 753145430616,2657317134051,9298091736000,32291110337661
%N A086603 a(n) = n^3*3^(n-1).
%C A086603 Binomial transform of A086604. Second binomial transform of A086605.
%H A086603 G. C. Greubel, <a href="/A086603/b086603.txt">Table of n, a(n) for n = 0..1000</a>
%H A086603 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-54,108,-81).
%F A086603 From _G. C. Greubel_, Feb 08 2020: (Start)
%F A086603 G.f.: x*(1 + 12*x + 9*x^2)/(1-3*x)^4.
%F A086603 E.g.f.: x*(1 + 9*x + 9*x^2)*exp(x). (End)
%p A086603 seq( 3^(n-1)*n^3, n=0..30); # _G. C. Greubel_, Feb 08 2020
%t A086603 Table[n^3 3^(n-1),{n,0,30}]  (* _Harvey P. Dale_, Mar 12 2011 *)
%o A086603 (PARI) vector(31, n, my(m=n-1); 3^(m-1)*m^3) \\ _G. C. Greubel_, Feb 08 2020
%o A086603 (Magma) [3^(n-1)*n^3: n in [0..30]]; // _G. C. Greubel_, Feb 08 2020
%o A086603 (Sage) [3^(n-1)*n^3 for n in (0..30)] # _G. C. Greubel_, Feb 08 2020
%o A086603 (GAP) List([0..30], n-> 3^(n-1)*n^3 ); # _G. C. Greubel_, Feb 08 2020
%Y A086603 Cf. A014477, A086604, A086605.
%K A086603 easy,nonn
%O A086603 0,3
%A A086603 _Paul Barry_, Jul 23 2003