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 A387229 #19 Aug 24 2025 03:52:30
%S A387229 1,22,343,4604,56765,662450,7438515,81174840,866564025,9090485390,
%T A387229 94014360143,960890353076,9723664642549,97564323687082,
%U A387229 971756818248235,9616894723897200,94635806917660785,926607762721058310,9032093873432341575,87685949210949054060,848182216775168898861
%N A387229 Expansion of sqrt((1-x) / (1-9*x)^5).
%H A387229 Vincenzo Librandi, <a href="/A387229/b387229.txt">Table of n, a(n) for n = 0..500</a>
%F A387229 n*a(n) = (10*n+12)*a(n-1) - 9*n*a(n-2) for n > 1.
%F A387229 a(n) = (1/4)^n * Sum_{k=0..n} 9^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387229 a(n) = Sum_{k=0..n} 2^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+1,n-k).
%F A387229 a(n) = Sum_{k=0..n} (-2)^k * 9^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n+1,n-k).
%F A387229 a(n) ~ 2^(7/2) * n^(3/2) * 3^(2*n-2) / sqrt(Pi). - _Vaclav Kotesovec_, Aug 24 2025
%t A387229 CoefficientList[Series[Sqrt[(1-x)/(1-9*x)^5],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387229 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-x)/(1-9*x)^5))
%o A387229 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- x) / (1-9*x)^5); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387229 Cf. A387228, A387230.
%Y A387229 Cf. A085363, A387208.
%K A387229 nonn,new
%O A387229 0,2
%A A387229 _Seiichi Manyama_, Aug 23 2025