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 A383597 #21 May 04 2025 15:07:13
%S A383597 1,4,25,190,1570,13552,120178,1085620,9940345,91962460,857750233,
%T A383597 8053389142,76026759760,721017894640,6864725124520,65578937628304,
%U A383597 628320730656586,6035594205744520,58110220504754650,560624083417180300,5418599393597801020,52459116546784350880
%N A383597 Expansion of 1/( (1-x)^2 * (1-10*x) )^(1/3).
%H A383597 Vincenzo Librandi, <a href="/A383597/b383597.txt">Table of n, a(n) for n = 0..300</a>
%F A383597 a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n,k).
%F A383597 n*a(n) = (11*n-7)*a(n-1) - 10*(n-1)*a(n-2) for n > 1.
%F A383597 a(n) ~ 10^(n + 2/3) / (Gamma(1/3) * 3^(4/3) * n^(2/3)). - _Vaclav Kotesovec_, May 02 2025
%F A383597 a(n) = hypergeom([1/3, -n], [1], -9). - _Stefano Spezia_, May 04 2025
%t A383597 Table[Sum[(-9)^k *Binomial[-1/3,k]* Binomial[n, k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, May 04 2025 *)
%o A383597 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-1/3, k)*binomial(n, k));
%o A383597 (Magma) I:=[4,25]; [1] cat [n le 2 select I[n] else ((11*n-7)*Self(n-1) - 10*(n-1) *Self(n-2))/n : n in [1..30]]; // _Vincenzo Librandi_, May 04 2025
%Y A383597 Cf. A383598, A383599.
%Y A383597 Cf. A004987, A361375, A376802, A383601.
%K A383597 nonn,easy
%O A383597 0,2
%A A383597 _Seiichi Manyama_, May 01 2025