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 A002570 M4090 N1698 #43 Jul 31 2024 04:10:07
%S A002570 1,1,6,11,36,85,235,600,1590,4140,10866,28416,74431,194821,510096,
%T A002570 1335395,3496170,9153025,23963005,62735880,164244756,429998256,
%U A002570 1125750156,2947252056,7716006181,20200766305,52886292930,138458112275,362488044120
%N A002570 From a definite integral.
%D A002570 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002570 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002570 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A002570 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A002570 L. R. Shenton, <a href="http://dx.doi.org/10.1017/S0013091500014280">A determinantal expansion for a class of definite integral. Part 5. Recurrence relations</a>, Proc. Edinburgh Math. Soc. (2) 10 (1957), 167-188.
%H A002570 L. R. Shenton and K. O. Bowman, <a href="http://www.pphmj.com/abstract/901.htm">Second order continued fractions and Fibonacci numbers</a>, Far East Journal of Applied Mathematics, 20(1), 17-31, 2005.
%F A002570 a(n) = a(n-2) + A002571(n-1), n > 2. - _Sean A. Irvine_, Apr 09 2014
%F A002570 a(2*n-2) = Sum_{k=0..n} k*Fibonacci(2*n-2*k), n > 1. - _Greg Dresden_, Dec 02 2021
%p A002570 A002570:=-1/(z-1)/(z**2-3*z+1)/(1+z)**3; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%K A002570 nonn
%O A002570 1,3
%A A002570 _N. J. A. Sloane_
%E A002570 More terms from _Sean A. Irvine_, Apr 09 2014