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 A382543 #16 May 13 2025 02:44:00
%S A382543 1,2,9,58,428,3360,27295,226538,1907889,16239034,139326959,1202856930,
%T A382543 10436521180,90920984306,794767853334,6967126281976,61224158085137,
%U A382543 539141091531558,4756357637006941,42028309478725094,371898032568193530,3294977494088601508
%N A382543 Expansion of 1/(1 - x/(1 - 9*x)^(1/3))^2.
%H A382543 Vincenzo Librandi, <a href="/A382543/b382543.txt">Table of n, a(n) for n = 0..600</a>
%F A382543 a(n) = Sum_{k=0..n} 9^(n-k) * (k+1) * binomial(n-2*k/3-1,n-k).
%F A382543 D-finite with recurrence (n-1)*(n-2)*a(n) -3*(n-2)*(11*n-29)*a(n-1) +135*(n-3)*(3*n-10)*a(n-2) +(-2188*n^2+17739*n-35909)*a(n-3) +3*(1466*n^2-14601*n+36292)*a(n-4) +27*(-7*n^2+37*n-42)*a(n-5) +54*(3*n-10)*(3*n-14)*a(n-6)=0. - _R. J. Mathar_, Apr 02 2025
%t A382543 Table[Sum[9^(n-k)* (k+1)* Binomial[n-2*k/3-1, n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, May 12 2025 *)
%o A382543 (PARI) a(n) = sum(k=0, n, 9^(n-k)*(k+1)*binomial(n-2*k/3-1, n-k));
%o A382543 (Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/(1 - x/(1 - 9*x)^(1/3))^2)); // _Vincenzo Librandi_, May 12 2025
%Y A382543 Cf. A362206, A382544.
%K A382543 nonn,easy
%O A382543 0,2
%A A382543 _Seiichi Manyama_, Mar 31 2025