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 A387234 #17 Aug 23 2025 14:44:54
%S A387234 1,16,187,1908,18015,161700,1400385,11808480,97533075,792374720,
%T A387234 6350977457,50334074972,395137260609,3076728075036,23787996024015,
%U A387234 182783869074000,1396834725138435,10622886492055680,80436297856668225,606683298398776620,4559675718517366461
%N A387234 Expansion of sqrt((1-3*x) / (1-7*x)^5).
%H A387234 Vincenzo Librandi, <a href="/A387234/b387234.txt">Table of n, a(n) for n = 0..500</a>
%F A387234 n*a(n) = (10*n+6)*a(n-1) - 21*n*a(n-2) for n > 1.
%F A387234 a(n) = (1/4)^n * Sum_{k=0..n} 7^k * 3^(n-k) * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387234 a(n) = Sum_{k=0..n} 3^(n-k) * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+1,n-k).
%F A387234 a(n) = Sum_{k=0..n} (-1)^k * 7^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n+1,n-k).
%t A387234 CoefficientList[Series[Sqrt[(1-3*x)/(1-7*x)^5],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387234 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-3*x)/(1-7*x)^5))
%o A387234 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- 3*x) / (1-7*x)^5); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387234 Cf. A387228, A387233.
%Y A387234 Cf. A360318, A387212.
%K A387234 nonn,new
%O A387234 0,2
%A A387234 _Seiichi Manyama_, Aug 23 2025