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.

A173187 a(n) = binomial(n + 3, 3)*9^n.

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%I A173187 #27 Aug 28 2022 08:30:52
%S A173187 1,36,810,14580,229635,3306744,44641044,573956280,7102708965,
%T A173187 85232507580,997220338686,11422705697676,128505439098855,
%U A173187 1423444863864240,15556218869373480,168007163789233584
%N A173187 a(n) = binomial(n + 3, 3)*9^n.
%H A173187 Vincenzo Librandi, <a href="/A173187/b173187.txt">Table of n, a(n) for n = 0..400</a>
%H A173187 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (36,-486,2916,-6561).
%F A173187 From _Harvey P. Dale_, May 19 2011: (Start)
%F A173187 a(n) = 36*a(n-1)-486*a(n-2)+ 2916*a(n-3)-6561*a(n-4).
%F A173187 G.f.: 1/(1-9*x)^4. (End)
%F A173187 From _Amiram Eldar_, Aug 28 2022: (Start)
%F A173187 Sum_{n>=0} 1/a(n) = 1728*log(9/8) - 405/2.
%F A173187 Sum_{n>=0} (-1)^n/a(n) = 2700*log(10/9) - 567/2. (End)
%p A173187 A173187:=n->binomial(n+3,3)*9^n: seq(A173187(n), n=0..30); # _Wesley Ivan Hurt_, Jul 24 2017
%t A173187 Table[Binomial[n + 3, 3]*9^n, {n, 0, 20}]
%t A173187 LinearRecurrence[{36,-486,2916,-6561},{1,36,810,14580},30] (* _Harvey P. Dale_, May 19 2011 *)
%o A173187 (Magma) [Binomial(n+3, 3)*9^n: n in [0..20]]; // _Vincenzo Librandi_, Oct 13 2011
%o A173187 (PARI) a(n)=binomial(n+3,3)*9^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A173187 Cf. A081139, A173000.
%K A173187 nonn,easy
%O A173187 0,2
%A A173187 _Zerinvary Lajos_, Feb 12 2010