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 A387208 #17 Aug 23 2025 07:57:34
%S A387208 1,13,145,1517,15329,151565,1476465,14228205,135990465,1291409165,
%T A387208 12199991633,114761111789,1075651464865,10051341904141,93677905064497,
%U A387208 871083359663085,8083754402585985,74885500462111245,692624008942816785,6397104350057979885,59008673876627412321
%N A387208 Expansion of sqrt((1-x) / (1-9*x)^3).
%H A387208 Vincenzo Librandi, <a href="/A387208/b387208.txt">Table of n, a(n) for n = 0..300</a>
%F A387208 n*a(n) = (10*n+3)*a(n-1) - 9*(n-1)*a(n-2) for n > 1.
%F A387208 a(n) = (1/4)^n * Sum_{k=0..n} 9^k * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387208 a(n) = Sum_{k=0..n} 2^k * (2*k+1) * binomial(2*k,k) * binomial(n,n-k).
%F A387208 a(n) = Sum_{k=0..n} (-2)^k * 9^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n,n-k).
%F A387208 a(n) ~ 2^(5/2) * sqrt(n) * 3^(2*n-1) / sqrt(Pi). - _Vaclav Kotesovec_, Aug 23 2025
%t A387208 CoefficientList[Series[Sqrt[(1-x)/(1-9*x)^3],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387208 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-x)/(1-9*x)^3))
%o A387208 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1-x) / (1-9*x)^3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387208 Cf. A163869, A163872, A387210.
%Y A387208 Cf. A085363, A383946.
%K A387208 nonn,new
%O A387208 0,2
%A A387208 _Seiichi Manyama_, Aug 22 2025