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 A361791 #22 Jul 12 2024 16:39:52
%S A361791 1,2,-4,-10,30,72,-238,-580,1970,4910,-16734,-42750,144600,379000,
%T A361791 -1264700,-3402480,11160730,30828070,-99168820,-281279030,885931600,
%U A361791 2580541580,-7948885910,-23779051760,71572652480,219906488302,-646332447086,-2039738985238,5850898295170
%N A361791 Expansion of 1/sqrt(1 - 4*x/(1+x)^5).
%H A361791 Winston de Greef, <a href="/A361791/b361791.txt">Table of n, a(n) for n = 0..2034</a>
%F A361791 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n+4*k-1,n-k).
%F A361791 n*a(n) = -( (2*n-4)*a(n-1) + (11*n-14)*a(n-2) + 20*(n-3)*a(n-3) + 15*(n-4)*a(n-4) + 6*(n-5)*a(n-5) + (n-6)*a(n-6) ) for n > 5.
%F A361791 a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+k) * binomial(n+3-k,4) * a(k).
%F A361791 a(n) = (-1)^(n+1)*Pochhammer(n,4)*hypergeom([3/2, 1-n, 1+n/4, (5+n)/4, (6+n)/4, (7+n)/4], [6/5, 7/5, 8/5, 9/5, 2], 2^10/5^5)/12 for n > 0. - _Stefano Spezia_, Jul 11 2024
%t A361791 a[n_]:=(-1)^(n+1)Pochhammer[n,4]HypergeometricPFQ[{3/2,1-n,1+n/4,(5+n)/4, (6+n)/4, (7+n)/4}, {6/5,7/5,8/5,9/5,2}, 2^10/5^5]/12; Join[{1},Array[a,28]] (* _Stefano Spezia_, Jul 11 2024 *)
%o A361791 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x)^5))
%o A361791 (PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(2*k,k) * binomial(n+4*k-1,n-k)) \\ _Winston de Greef_, Mar 24 2023
%Y A361791 Cf. A006139, A137635, A360133, A361790, A361792.
%Y A361791 Cf. A359758.
%K A361791 sign
%O A361791 0,2
%A A361791 _Seiichi Manyama_, Mar 24 2023