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 A383601 #21 May 05 2025 11:45:45
%S A383601 1,7,58,514,4705,43879,414208,3943492,37782346,363760390,3515819020,
%T A383601 34088616940,331383573010,3228590970430,31514912933800,
%U A383601 308126549765440,3016908101224105,29576113797737695,290271761086278610,2851684765215491050,28040613734007656545
%N A383601 Expansion of 1/( (1-x) * (1-10*x)^2 )^(1/3).
%H A383601 Vincenzo Librandi, <a href="/A383601/b383601.txt">Table of n, a(n) for n = 0..300</a>
%F A383601 a(n) = Sum_{k=0..n} (-9)^k * binomial(-2/3,k) * binomial(n,k).
%F A383601 n*a(n) = (11*n-4)*a(n-1) - 10*(n-1)*a(n-2) for n > 1.
%F A383601 a(n) ~ Gamma(1/3) * 2^(n - 2/3) * 5^(n + 1/3) / (Pi * 3^(1/6) * n^(1/3)). - _Vaclav Kotesovec_, May 02 2025
%F A383601 a(n) = hypergeom([2/3, -n], [1], -9). - _Stefano Spezia_, May 04 2025
%t A383601 Table[Sum[(-9)^k* Binomial[-2/3,k]* Binomial[n,k],{k,0,n}],{n,0,22}] (* _Vincenzo Librandi_, May 05 2025 *)
%o A383601 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-2/3, k)*binomial(n, k));
%o A383601 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x) * (1-10*x)^2 )^(1/3))); // _Vincenzo Librandi_, May 05 2025
%Y A383601 Cf. A383605, A383606.
%Y A383601 Cf. A004988, A377233, A383597.
%K A383601 nonn,easy
%O A383601 0,2
%A A383601 _Seiichi Manyama_, May 01 2025