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 A383947 #17 Aug 28 2025 00:04:41
%S A383947 1,2,15,84,525,3318,21371,139240,915417,6060330,40345767,269825724,
%T A383947 1811432805,12200012958,82394389395,557794589904,3784079617713,
%U A383947 25718668160850,175085306697791,1193682452744740,8148955372804029,55697327430265158,381099865385716395
%N A383947 Expansion of 1/sqrt((1+x)^3 * (1-7*x)).
%H A383947 Vincenzo Librandi, <a href="/A383947/b383947.txt">Table of n, a(n) for n = 0..800</a>
%F A383947 n*a(n) = (6*n-4)*a(n-1) + 7*n*a(n-2) for n > 1.
%F A383947 a(n) = (1/4)^n * Sum_{k=0..n} (-1)^k * 7^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383947 a(n) = Sum_{k=0..n} (-2)^k * 7^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+1,n-k).
%F A383947 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(2*k,k) * binomial(n+1,n-k).
%t A383947 CoefficientList[Series[1/Sqrt[(1+x)^3*(1-7*x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383947 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1+x)^3*(1-7*x)))
%o A383947 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1+x)^3 * (1-7*x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383947 Cf. A085458, A322242.
%K A383947 nonn,changed
%O A383947 0,2
%A A383947 _Seiichi Manyama_, Aug 19 2025