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 A027476 #22 Sep 08 2022 08:44:49
%S A027476 1,45,1350,33750,759375,15946875,318937500,6150937500,115330078125,
%T A027476 2114384765625,38058925781250,674680957031250,11806916748046875,
%U A027476 204350482177734375,3503151123046875000,59553569091796875000
%N A027476 Third column of A027467.
%H A027476 Vincenzo Librandi, <a href="/A027476/b027476.txt">Table of n, a(n) for n = 3..200</a>
%H A027476 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (45,-675,3375).
%F A027476 Numerators of sequence a[3,n] in (a[i,j])^4 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
%F A027476 a(n) = 15^(n-3)*binomial(n-1, 2).
%F A027476 From _G. C. Greubel_, May 13 2021: (Start)
%F A027476 a(n) = 45*a(n-1) - 675*a(n-2) + 3375*a(n-3).
%F A027476 G.f.: x^3/(1 - 15*x)^3.
%F A027476 E.g.f.: (-2 + (2 - 30*x + 225*x^2)*exp(15*x))/6750. (End)
%F A027476 From _Amiram Eldar_, Jan 06 2022: (Start)
%F A027476 Sum_{n>=3} 1/a(n) = 30 - 420*log(15/14).
%F A027476 Sum_{n>=3} (-1)^(n+1)/a(n) = 480*log(16/15) - 30. (End)
%p A027476 seq((15)^(n-3)*binomial(n-1, 2), n=3..30) # _G. C. Greubel_, May 13 2021
%t A027476 Table[(n-1)*(n-2)/2 * 15^(n-3), {n, 3, 30}] (* _Vincenzo Librandi_, Dec 29 2012 *)
%o A027476 (Magma) [(n-1)*(n-2)/2 * 15^(n-3): n in [3..20]]; // _Vincenzo Librandi_, Dec 29 2012
%o A027476 (Sage) [(15)^(n-3)*binomial(n-1,2) for n in (3..30)] # _G. C. Greubel_, May 13 2021
%Y A027476 Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), this sequence (q=15).
%K A027476 nonn
%O A027476 3,2
%A A027476 _Olivier Gérard_