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 A387233 #17 Aug 23 2025 10:02:09
%S A387233 1,14,142,1252,10190,78724,586236,4247688,30132438,210175540,
%T A387233 1445920388,9833940472,66237449356,442463439656,2934485313400,
%U A387233 19340115356688,126759642351462,826734451831956,5368338057048756,34721155684000920,223765535492622564,1437403425873718776
%N A387233 Expansion of sqrt((1-2*x) / (1-6*x)^5).
%H A387233 Vincenzo Librandi, <a href="/A387233/b387233.txt">Table of n, a(n) for n = 0..500</a>
%F A387233 n*a(n) = (8*n+6)*a(n-1) - 12*n*a(n-2) for n > 1.
%F A387233 a(n) = (1/2)^n * Sum_{k=0..n} 3^k * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k)/(1-2*(n-k)).
%F A387233 a(n) = Sum_{k=0..n} 2^(n-k) * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+1,n-k).
%F A387233 a(n) = Sum_{k=0..n} (-1)^k * 6^(n-k) * binomial(2*k,k)/(1-2*k) * binomial(n+1,n-k).
%t A387233 CoefficientList[Series[Sqrt[(1-2*x)/(1-6*x)^5],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 23 2025 *)
%o A387233 (PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-2*x)/(1-6*x)^5))
%o A387233 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := Sqrt((1- 2*x) / (1-6*x)^5); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 23 2025
%Y A387233 Cf. A387228, A387234.
%Y A387233 Cf. A360317, A387211.
%K A387233 nonn,new
%O A387233 0,2
%A A387233 _Seiichi Manyama_, Aug 23 2025