# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a361792
Showing 1-1 of 1

%I A361792 #23 Jul 12 2024 16:40:53
%S A361792 1,2,-6,-10,66,60,-750,-236,8682,-2098,-100792,80286,1162458,-1603412,
%T A361792 -13225764,26767020,147428498,-409582818,-1596563202,5941802122,
%U A361792 16587101544,-83014131140,-161717252990,1126247965980,1411774064970,-14905602076350
%N A361792 Expansion of 1/sqrt(1 - 4*x/(1+x)^6).
%H A361792 Seiichi Manyama, <a href="/A361792/b361792.txt">Table of n, a(n) for n = 0..1000</a>
%F A361792 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n+5*k-1,n-k).
%F A361792 n*a(n) = -( (3*n-5)*a(n-1) + (17*n-24)*a(n-2) + 35*(n-3)*a(n-3) + 35*(n-4)*a(n-4) + 21*(n-5)*a(n-5) + 7*(n-6)*a(n-6) + (n-7)*a(n-7) ) for n > 6.
%F A361792 a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+k) * binomial(n+4-k,5) * a(k).
%F A361792 a(n) = (-1)^(n+1)*Pochhammer(n,5)*hypergeom([1-n, 1+n/5, (6+n)/5, (7+n)/5, (8+n)/5, (9+n)/5], [7/6, 4/3, 5/3, 11/6, 2], 5^5/(2^4*3^6))/60 for n > 0. - _Stefano Spezia_, Jul 11 2024
%t A361792 a[n_]:=(-1)^(n+1)Pochhammer[n,5]HypergeometricPFQ[{1-n,1+n/5,(6+n)/5, (7+n)/5, (8+n)/5, (9+n)/5}, {7/6,4/3,5/3,11/6,2}, 5^5/(2^4*3^6)]/60; Join[{1},Array[a,25]] (* _Stefano Spezia_, Jul 11 2024 *)
%o A361792 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x)^6))
%Y A361792 Cf. A006139, A137635, A360133, A361790, A361791.
%Y A361792 Cf. A360132.
%K A361792 sign
%O A361792 0,2
%A A361792 _Seiichi Manyama_, Mar 24 2023

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE