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 A387228 #20 Aug 24 2025 04:12:45
%S A387228 1,12,103,764,5215,33728,210021,1271504,7532547,43859460,251809701,
%T A387228 1428911652,8028877233,44734340784,247433518875,1359902816880,
%U A387228 7432212863235,40416897046740,218812616979845,1179889937796900,6339243523221245,33947223885549040,181245459484155935
%N A387228 Expansion of sqrt((1-x) / (1-5*x)^5).
%H A387228 Vincenzo Librandi, <a href="/A387228/b387228.txt">Table of n, a(n) for n = 0..500</a>
%F A387228 n*a(n) = (6*n+6)*a(n-1) - 5*n*a(n-2) for n > 1.
%F A387228 a(n) = (1/4)^n * Sum_{k=0..n} 5^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387228 a(n) = Sum_{k=0..n} ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+1,n-k).
%F A387228 a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n+1,n-k).
%F A387228 a(n) ~ 8 * 5^(n - 1/2) * n^(3/2) / (3*sqrt(Pi)). - _Vaclav Kotesovec_, Aug 23 2025
%t A387228 CoefficientList[Series[Sqrt[(1-x)/(1-5*x)^5],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 24 2025 *)
%o A387228 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-x)/(1-5*x)^5))
%o A387228 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- x) / (1-5*x)^5); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 24 2025
%Y A387228 Cf. A387229, A387230.
%Y A387228 Cf. A085362, A163869.
%Y A387228 Cf. A377199.
%K A387228 nonn,new
%O A387228 0,2
%A A387228 _Seiichi Manyama_, Aug 23 2025