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 A257859 #42 Sep 08 2022 08:46:12
%S A257859 2,1,1,4,27,239,2602,33587,501203,8486864,160749213,3367246609,
%T A257859 77285922794,1928780823241,51999796304713,1506065312013436,
%U A257859 46636024876111803,1537482755599676063,53765260421112550402,1987777152825564688811,77469543699775910313227
%N A257859 a(n) = (2*n-1)*a(n-1) - a(n-2) with a(0)=2, a(1)=1.
%F A257859 a(n) = 2*A053983(n) - A053984(n).
%F A257859 a(n) = (SBY(0,1) - 2*SBY(1,1))*SBJ(n,1) - (SBJ(0,1) - 2*SBJ(1,1))*SBY(n,1), where SBJ and SBY are the spherical Bessel functions of first and second kind, respectively.
%F A257859 E.g.f.: (2*cos(1-sqrt(1-2*x)) - sin(1-sqrt(1-2*x)))/sqrt(1-2*x).
%F A257859 Sum_{n=0..infinity} a(n-1) x^n/n! = cos(1-sqrt(1-2*x)) + 2*sin(1-sqrt(1-2*x)), where a(-1)=1, a(0)=2, a(1)=1.
%F A257859 a(n) ~ (2*cos(1)-sin(1)) * 2^(n+1/2) * n^n / exp(n). - _Vaclav Kotesovec_, May 20 2015
%t A257859 RecurrenceTable[{a[0] == 2, a[1] == 1, a[n] == -a[n - 2] + (2 n - 1) a[n - 1]}, a, {n, 30}]
%o A257859 (Magma) [n le 2 select 3-n else (2*n-3)*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, May 12 2015
%Y A257859 Cf. A053983, A053984.
%K A257859 nonn,easy
%O A257859 0,1
%A A257859 _G. C. Greubel_, May 10 2015