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 A387212 #17 Aug 23 2025 14:44:50
%S A387212 1,9,75,599,4659,35595,268485,2005785,14873715,109643195,804354417,
%T A387212 5877232773,42798735805,310767250773,2250899498763,16267896905895,
%U A387212 117347641620435,845043416086635,6076092412278465,43629213402099045,312892629725930121,2241442380182752209
%N A387212 Expansion of sqrt((1-3*x) / (1-7*x)^3).
%H A387212 Vincenzo Librandi, <a href="/A387212/b387212.txt">Table of n, a(n) for n = 0..500</a>
%F A387212 n*a(n) = (10*n-1)*a(n-1) - 21*(n-1)*a(n-2) for n > 1.
%F A387212 a(n) = (1/4)^n * Sum_{k=0..n} 7^k * 3^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387212 a(n) = Sum_{k=0..n} 3^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n,n-k).
%F A387212 a(n) = Sum_{k=0..n} (-1)^k * 7^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n,n-k).
%t A387212 CoefficientList[Series[Sqrt[(1-3*x)/(1-7*x)^3],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387212 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-3*x)/(1-7*x)^3))
%o A387212 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- 3*x) / (1-7*x)^3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387212 Cf. A163869, A387211.
%Y A387212 Cf. A360318, A385813.
%K A387212 nonn,new
%O A387212 0,2
%A A387212 _Seiichi Manyama_, Aug 22 2025