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 A383945 #16 Aug 28 2025 00:04:46
%S A383945 1,17,206,2150,20615,187103,1633996,13868508,115147965,939490365,
%T A383945 7557020922,60073436514,472815344547,3689827880235,28584232842840,
%U A383945 220017882647544,1683964821974073,12824134005685929,97224403777732070,734127854369080990,5523136813883811199
%N A383945 Expansion of 1/sqrt((1-7*x)^5 * (1+x)).
%H A383945 Vincenzo Librandi, <a href="/A383945/b383945.txt">Table of n, a(n) for n = 0..800</a>
%F A383945 n*a(n) = (6*n+11)*a(n-1) + 7*(n+1)*a(n-2) for n > 1.
%F A383945 a(n) = (1/4)^n * Sum_{k=0..n} 7^k * (-1)^(n-k) * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383945 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * ((2*k+1) * (2*k+3)/3) * binomial(2*k,k) * binomial(n+2,n-k).
%F A383945 a(n) = Sum_{k=0..n} (-2)^k * 7^(n-k) * binomial(2*k,k) * binomial(n+2,n-k).
%t A383945 CoefficientList[Series[1/Sqrt[(1-7*x)^5*(1+x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383945 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-7*x)^5*(1+x)))
%o A383945 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1-7*x)^5 * (1+x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383945 Cf. A322242, A383944.
%K A383945 nonn,changed
%O A383945 0,2
%A A383945 _Seiichi Manyama_, Aug 19 2025