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 A383602 #22 May 05 2025 16:21:48
%S A383602 1,7,55,453,3819,32637,281409,2441715,21285411,186225253,1633973125,
%T A383602 14370441055,126631522005,1117707358515,9879287145855,87428272217853,
%U A383602 774533435844531,6868083093333285,60952616213098789,541342619512077967,4811079933571973329
%N A383602 Expansion of 1/( (1-x) * (1-9*x)^3 )^(1/4).
%H A383602 Vincenzo Librandi, <a href="/A383602/b383602.txt">Table of n, a(n) for n = 0..300</a>
%F A383602 a(n) = Sum_{k=0..n} (-8)^k * binomial(-3/4,k) * binomial(n,k).
%F A383602 n*a(n) = (10*n-3)*a(n-1) - 9*(n-1)*a(n-2) for n > 1.
%F A383602 a(n) ~ Gamma(1/4) * 3^(2*n + 1/2) / (Pi * 2^(5/4) * n^(1/4)). - _Vaclav Kotesovec_, May 02 2025
%F A383602 a(n) = hypergeom([3/4, -n], [1], -8). - _Stefano Spezia_, May 05 2025
%t A383602 Table[Sum[(-8)^k* Binomial[-3/4,k]* Binomial[n,k],{k,0,n}],{n,0,22}] (* _Vincenzo Librandi_, May 05 2025 *)
%o A383602 (PARI) a(n) = sum(k=0, n, (-8)^k*binomial(-3/4, k)*binomial(n, k));
%o A383602 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x) * (1-9*x)^3 )^(1/4))); // _Vincenzo Librandi_, May 05 2025
%Y A383602 Cf. A084771, A383600.
%Y A383602 Cf. A004982.
%K A383602 nonn,easy
%O A383602 0,2
%A A383602 _Seiichi Manyama_, May 01 2025