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 A382544 #18 Apr 01 2025 08:56:24
%S A382544 1,3,15,100,753,6006,49456,415422,3536802,30404161,263271639,
%T A382544 2292524970,20052238465,176029542285,1549916592645,13681091072620,
%U A382544 121020187476717,1072477163769417,9519299301332377,84609930915003882,752947626436806021,6707715814093174588
%N A382544 Expansion of 1/(1 - x/(1 - 9*x)^(1/3))^3.
%H A382544 Vincenzo Librandi, <a href="/A382544/b382544.txt">Table of n, a(n) for n = 0..300</a>
%F A382544 a(n) = Sum_{k=0..n} 9^(n-k) * binomial(k+2,2) * binomial(n-2*k/3-1,n-k).
%t A382544 Table[Sum[9^(n-k)*Binomial[k+2,2]* Binomial [n-2*k/3-1, n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Mar 31 2025 *)
%o A382544 (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(k+2, 2)*binomial(n-2*k/3-1, n-k));
%o A382544 (Magma) R<x> := PowerSeriesRing(Rationals(), 25);f := x / (1 - 9*x)^(1/3);G := 1 / (1 - f)^3;Coefficients(G); // _Vincenzo Librandi_, Mar 31 2025
%Y A382544 Cf. A362206, A382543.
%K A382544 nonn,easy
%O A382544 0,2
%A A382544 _Seiichi Manyama_, Mar 31 2025