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 A383892 #18 May 28 2025 18:39:57
%S A383892 1,25,355,3775,33502,262570,1880090,12574850,79778303,485441135,
%T A383892 2856558005,16358449625,91615095204,503740623720,2727832278900,
%U A383892 14584759018500,77152991893005,404503014170325,2104862289863575,10883633564375875,55976319375728506,286601257317512950
%N A383892 Expansion of 1/( ((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 * (1-5*x) ).
%H A383892 Vincenzo Librandi, <a href="/A383892/b383892.txt">Table of n, a(n) for n = 0..500</a>
%H A383892 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (25,-270,1650,-6273,15345,-24080,23300,-12576,2880).
%F A383892 a(n) = 25*a(n-1) - 270*a(n-2) + 1650*a(n-3) - 6273*a(n-4) + 15345*a(n-5) - 24080*a(n-6) + 23300*a(n-7) - 12576*a(n-8) + 2880*a(n-9).
%F A383892 a(n) = Sum_{k=0..n} Stirling2(k+4,4) * Stirling2(n-k+5,5).
%t A383892 a[n_]:=Sum [StirlingS2[k+4,4]*StirlingS2[n-k+5,5],{k,0,n}];Table[a[n],{n,0,19}] (* _Vincenzo Librandi_, May 23 2025 *)
%o A383892 (PARI) a(n) = sum(k=0, n, stirling(k+4, 4, 2)*stirling(n-k+5, 5, 2));
%o A383892 (Magma) [1] cat [&+[StirlingSecond(k+4,4) * StirlingSecond(n-k+5,5): k in [0..n]]: n in [1..25]]; // _Vincenzo Librandi_, May 23 2025
%Y A383892 Column k=5 of A287532.
%Y A383892 Cf. A383842.
%K A383892 nonn,easy
%O A383892 0,2
%A A383892 _Seiichi Manyama_, May 14 2025