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 A058799 #35 Feb 16 2025 08:32:43
%S A058799 1,3,11,52,301,2055,16139,143196,1415821,15430835,183754199,
%T A058799 2373373752,33043478329,493278801183,7859417340599,133116815989000,
%U A058799 2388243270461401,45243505322777619,902481863185090979
%N A058799 Column 2 of A007754.
%C A058799 Conjectured partial sums of A093935. - _Sean A. Irvine_, Jun 25 2022
%H A058799 Seiichi Manyama, <a href="/A058799/b058799.txt">Table of n, a(n) for n = 0..448</a>
%H A058799 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModularGroupGamma.html">Modular Group Gamma</a>. [_Roger L. Bagula_, Nov 02 2008]
%F A058799 a(n) = (n+2)*a(n-1)-a(n-2) [with a(0)=1 and a(-1)=0] = A058798(n+1) - A058797(n+2). - _Henry Bottomley_, Feb 28 2001
%F A058799 A signed version with a slightly different start may be obtained from the modular group Gamma: Let S = {{0, -1}, {1, 0}}; T = {{1, 1}, {0, 1}}; m(n) = T^n.S.m(m-1); v(0)={1,0}; v(n)=m(n).v(0); a(n)=v(n)[[1]]. This gives the sequence 1, 0, -1, -3, -11, -52, -301, -2055, -16139, -143196, -1415821, -15430835, ... - _Roger L. Bagula_, Nov 02 2008
%F A058799 a(n) = Sum_{k = 0..floor(n/2)} (-1)^k*(n-2*k)!*binomial(n-k,k)*binomial(n-k+2,k+2). Cf. A058798. - _Peter Bala_, Aug 01 2013
%t A058799 Clear[S, T, M, v, n]; S = {{0, -1}, {1, 0}}; T = {{1, 1}, {0, 1}}; M[0] = T.S; M[n_] := M[n] = (MatrixPower[T, n].S).M[n - 1]; v[0] = {1, 0}; v[n_] := v[n] = M[n].v[0]; a = Table[v[n][[1]], {n, 0, 30}] (* _Roger L. Bagula_, Nov 02 2008 *)
%t A058799 nxt[{n_,a_,b_}]:={n+1,b,(n+3)b-a}; NestList[nxt,{0,0,1},20][[;;,2]] (* _Harvey P. Dale_, Jul 30 2023 *)
%Y A058799 Cf. A007754, A058798.
%K A058799 nonn
%O A058799 0,2
%A A058799 _Christian G. Bower_, Dec 02 2000