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 A383949 #17 Aug 27 2025 14:11:16
%S A383949 1,4,15,60,255,1128,5117,23600,110115,518220,2455101,11693124,
%T A383949 55934385,268535400,1293178275,6243968880,30217425795,146529719100,
%U A383949 711810105725,3463284659300,16874328961245,82322471522280,402079323279975,1965900162652800,9621179345962525,47127880914834148
%N A383949 Expansion of 1/sqrt((1-x)^3 * (1-5*x)).
%H A383949 Vincenzo Librandi, <a href="/A383949/b383949.txt">Table of n, a(n) for n = 0..1000</a>
%F A383949 n*a(n) = (6*n-2)*a(n-1) - 5*n*a(n-2) for n > 1.
%F A383949 a(n) = (1/4)^n * Sum_{k=0..n} 5^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383949 a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+1,n-k).
%F A383949 a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+1,n-k).
%t A383949 CoefficientList[Series[1/Sqrt[(1-x)^3*(1-5*x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383949 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x)^3*(1-5*x)))
%o A383949 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1- x)^3 * (1-5*x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383949 Cf. A383948, A383950.
%Y A383949 Cf. A052244.
%K A383949 nonn,changed
%O A383949 0,2
%A A383949 _Seiichi Manyama_, Aug 19 2025