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 A382615 #19 Apr 02 2025 07:07:50
%S A382615 1,3,15,64,261,1032,3982,15066,56094,206068,748452,2691966,9600233,
%T A382615 33982197,119495229,417724302,1452550371,5026878774,17321417650,
%U A382615 59450099958,203306331429,692955932103,2354664287943,7978488379398,26963061909228,90897971951727
%N A382615 Expansion of 1/(1 - x/(1 - x)^3)^3.
%H A382615 Vincenzo Librandi, <a href="/A382615/b382615.txt">Table of n, a(n) for n = 0..400</a>
%H A382615 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12,-57,139,-195,174,-102,39,-9,1).
%F A382615 a(n) = Sum_{k=0..n} binomial(k+2,2) * binomial(n+2*k-1,n-k).
%F A382615 a(n) = 12*a(n-1) - 57*a(n-2) + 139*a(n-3) - 195*a(n-4) + 174*a(n-5) - 102*a(n-6) + 39*a(n-7) - 9*a(n-8) + a(n-9) for n > 9.
%t A382615 Table[Sum[Binomial[k+2,2]*Binomial[n+2*k-1,n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Apr 02 2025 *)
%o A382615 (PARI) a(n) = sum(k=0, n, binomial(k+2, 2)*binomial(n+2*k-1, n-k));
%o A382615 (Magma) R<x> := PowerSeriesRing(Rationals(), 40); f := 1/(1 - x/(1 - x)^3)^3; seq := [ Coefficient(f, n) : n in [0..30] ]; seq;// _Vincenzo Librandi_, Apr 02 2025
%Y A382615 Cf. A000217, A058396, A290918.
%Y A382615 Cf. A052529, A382616.
%Y A382615 Cf. A290917.
%K A382615 nonn,easy
%O A382615 0,2
%A A382615 _Seiichi Manyama_, Mar 31 2025