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 A383600 #26 May 05 2025 11:45:21
%S A383600 1,3,15,97,699,5313,41689,334215,2721411,22423737,186497325,
%T A383600 1562826195,13178010405,111700773135,951026829255,8128169277897,
%U A383600 69701329848051,599462375836185,5169038197383789,44674793959777443,386916485124220929,3357265884164614707
%N A383600 Expansion of 1/( (1-x)^3 * (1-9*x) )^(1/4).
%H A383600 Vincenzo Librandi, <a href="/A383600/b383600.txt">Table of n, a(n) for n = 0..300</a>
%F A383600 a(n) = Sum_{k=0..n} (-8)^k * binomial(-1/4,k) * binomial(n,k).
%F A383600 n*a(n) = (10*n-7)*a(n-1) - 9*(n-1)*a(n-2) for n > 1.
%F A383600 a(n) ~ 3^(2*n + 3/2) / (Gamma(1/4) * 2^(9/4) * n^(3/4)). - _Vaclav Kotesovec_, May 02 2025
%F A383600 a(n) = hypergeom([1/4, -n], [1], -8). - _Stefano Spezia_, May 05 2025
%t A383600 Table[Sum[(-8)^(k)* Binomial[-1/4,k]* Binomial[n,k],{k,0,n}],{n,0,22}] (* _Vincenzo Librandi_, May 05 2025 *)
%o A383600 (PARI) a(n) = sum(k=0, n, (-8)^k*binomial(-1/4, k)*binomial(n, k));
%o A383600 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x)^3 * (1-9*x) )^(1/4))); // _Vincenzo Librandi_, May 05 2025
%Y A383600 Cf. A084771, A383602.
%Y A383600 Cf. A004981, A231482.
%K A383600 nonn,easy
%O A383600 0,2
%A A383600 _Seiichi Manyama_, May 01 2025