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 A387230 #19 Aug 24 2025 03:50:03
%S A387230 1,32,723,14044,250415,4224732,68565049,1081299296,16679767923,
%T A387230 252819395920,3777709472537,55782986878164,815526073468561,
%U A387230 11821376147023268,170096339292264375,2431786467331116016,34569517907583692867,488963045591838160848,6885041951078984405449
%N A387230 Expansion of sqrt((1-x) / (1-13*x)^5).
%H A387230 Vincenzo Librandi, <a href="/A387230/b387230.txt">Table of n, a(n) for n = 0..500</a>
%F A387230 n*a(n) = (14*n+18)*a(n-1) - 13*n*a(n-2) for n > 1.
%F A387230 a(n) = (1/4)^n * Sum_{k=0..n} 13^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387230 a(n) = Sum_{k=0..n} 3^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+1,n-k).
%F A387230 a(n) = Sum_{k=0..n} (-3)^k * 13^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n+1,n-k).
%F A387230 a(n) ~ 8 * n^(3/2) * 13^(n - 1/2) / sqrt(3*Pi). - _Vaclav Kotesovec_, Aug 24 2025
%t A387230 CoefficientList[Series[Sqrt[(1-x)/(1-13*x)^5],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387230 (PARI) my(N=20, x='x+O('x^N)); Vec(sqrt((1-x)/(1-13*x)^5))
%o A387230 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- x) / (1-13*x)^5); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387230 Cf. A387228, A387229.
%Y A387230 Cf. A085364, A387210.
%K A387230 nonn,new
%O A387230 0,2
%A A387230 _Seiichi Manyama_, Aug 23 2025