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 A383950 #16 Aug 27 2025 11:29:07
%S A383950 1,6,30,148,750,3924,21084,115560,642582,3611140,20455908,116594328,
%T A383950 667851340,3840932424,22164538680,128269848528,744150592998,
%U A383950 4326419433060,25200835078164,147036927946680,859181709840804,5027183713857624,29450272491511560,172715082105669552
%N A383950 Expansion of 1/sqrt((1-2*x)^3 * (1-6*x)).
%H A383950 Vincenzo Librandi, <a href="/A383950/b383950.txt">Table of n, a(n) for n = 0..1000</a>
%F A383950 n*a(n) = (8*n-2)*a(n-1) - 12*n*a(n-2) for n > 1.
%F A383950 a(n) = (1/2)^n * Sum_{k=0..n} 3^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383950 a(n) = Sum_{k=0..n} (-1)^k * 6^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+1,n-k).
%F A383950 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*k,k) * binomial(n+1,n-k).
%t A383950 CoefficientList[Series[1/Sqrt[(1-2*x)^3*(1-6*x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383950 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-2*x)^3*(1-6*x)))
%o A383950 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1- 2*x)^3 * (1-6*x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383950 Cf. A383948, A383949.
%Y A383950 Cf. A231482.
%K A383950 nonn,changed
%O A383950 0,2
%A A383950 _Seiichi Manyama_, Aug 19 2025