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 A351825 #21 Mar 20 2023 08:56:14
%S A351825 0,0,2,6,36,260,2190,21042,226856,2709576,35491770,505620830,
%T A351825 7780224012,128555409996,2269569526406,42625044254730,848404205856720,
%U A351825 17836074466842512,394872870912995826,9181542826326252726,223680717959853460340,5697036951307194432660,151396442683371572351742
%N A351825 Total number of size 2 lists in all sets of lists partitioning [n] (cf. A000262).
%F A351825 a(n) = 2*binomial(n,2)*A000262(n-2).
%F A351825 E.g.f.: x^2*exp(x/(1-x)) = d/dy G(x,y)|y=1 where G(x,y) is the e.g.f. for A351823.
%F A351825 a(n) = Sum_{k=0..floor(n/2)} k * A351823(n,k).
%F A351825 a(n) ~ n^(n - 1/4) * exp(2*sqrt(n) - n - 1/2) / sqrt(2) * (1 - 101/(48*sqrt(n))). - _Vaclav Kotesovec_, Feb 21 2022
%F A351825 a(n) = 2 * A129652(n,2). - _Alois P. Heinz_, Feb 22 2022
%F A351825 Recurrence: (n-2)*a(n) = n*(2*n-5)*a(n-1) - (n-4)*(n-1)*n*a(n-2). - _Vaclav Kotesovec_, Mar 20 2023
%t A351825 nn = 22; Range[0, nn]! CoefficientList[Series[D[Exp[ x/(1 - x) - x ^2 + y x^2], y] /. y -> 1, {x, 0, nn}], x]
%t A351825 Join[{0, 0, 2}, Table[n!*Hypergeometric1F1[n-1, 2, 1]/E, {n, 3, 25}]] (* _Vaclav Kotesovec_, Feb 21 2022 *)
%Y A351825 Cf. A000262, A006152, A129652, A351823.
%K A351825 nonn
%O A351825 0,3
%A A351825 _Geoffrey Critzer_, Feb 20 2022