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 A122031 #29 Jan 05 2021 22:01:22
%S A122031 1,2,3,7,16,44,124,388,1256,4360,15664,59264,231568,942736,3953120,
%T A122031 17151424,76448224,350871008,1650490816,7966168960,39325494464,
%U A122031 198648873664,1024484257408,5394759478016,28957897398400
%N A122031 a(n) = a(n - 1) + (n - 1)*a(n - 2).
%C A122031 Equals the eigensequence of an infinite lower triangular matrix with (1, 1, 1, ...) in the main diagaonal, (1, 1, 2, 3, 4, 5, ...) in the subdiagonal and the rest zeros. - _Gary W. Adamson_, Apr 13 2009
%H A122031 G. C. Greubel, <a href="/A122031/b122031.txt">Table of n, a(n) for n = 0..795</a>
%F A122031 E.g.f.: (1/2)*exp(x + x^2/2)*(2 - sqrt(2*exp(1)*Pi)*erf(1/sqrt(2)) + sqrt(2*exp(1)*Pi)*erf((1+x)/sqrt(2))). - Paul Abbott (paul(AT) physics.uwa.edu.au)
%F A122031 a(n) ~ (1/sqrt(2) + sqrt(Pi)/2*exp(1/2) * (1 - erf(1/sqrt(2)))) * n^(n/2)*exp(sqrt(n) - n/2 - 1/4) * (1+7/(24*sqrt(n))). - _Vaclav Kotesovec_, Dec 27 2012
%t A122031 a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1] + (n - 1)*a[n - 2] Table[a[n], {n, 0, 30}]
%t A122031 Table[n!*SeriesCoefficient[1/2*Exp[x+x^2/2]*(2-Sqrt[2*E*Pi]*Erf[1/Sqrt[2]]+Sqrt[2*E*Pi]*Erf[(1+x)/Sqrt[2]]),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_ after Paul Abbott, Dec 27 2012 *)
%t A122031 RecurrenceTable[{a[0]==1,a[1]==2,a[n]==a[n-1]+(n-1)a[n-2]},a,{n,30}] (* _Harvey P. Dale_, Feb 21 2015 *)
%Y A122031 Cf. A000898, A062267, A121966, A122021, A122022.
%K A122031 nonn
%O A122031 0,2
%A A122031 _Roger L. Bagula_, Sep 13 2006
%E A122031 Edited by _N. J. A. Sloane_, Sep 17 2006
%E A122031 Offset corrected by _Vaclav Kotesovec_, Dec 27 2012