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 A260769 #16 Jul 15 2022 05:31:43 %S A260769 1,3,15,84,491,2948,18018,111520,696739,4384668,27753110,176494640, %T A260769 1126809230,7217773800,46364184420,298554038144,1926593569059, %U A260769 12455864623020,80664529969422,523165672201744,3397648036150426,22092460470618328,143809661629562460 %N A260769 Certain directed lattice paths. %C A260769 See Dziemianczuk (2014) for precise definition. %H A260769 Lars Blomberg, <a href="/A260769/b260769.txt">Table of n, a(n) for n = 0..100</a> %H A260769 M. Dziemianczuk, <a href="http://arxiv.org/abs/1410.5747">On Directed Lattice Paths With Additional Vertical Steps</a>, arXiv preprint arXiv:1410.5747 [math.CO], 2014. %F A260769 See Dziemianczuk (2014) Equation (29a) with m=0. %F A260769 From _Vaclav Kotesovec_, Jul 15 2022: (Start) %F A260769 Recurrence: (n-1)*n*(100*n^2 - 410*n + 411)*a(n) = -10*(n-1)*(8*n - 25)*a(n-1) + 4*(1100*n^4 - 6710*n^3 + 14571*n^2 - 13303*n + 4267)*a(n-2) - 120*(n-2)*(2*n - 1)*a(n-3) + 16*(n-3)*(n-2)*(100*n^2 - 210*n + 101)*a(n-4). %F A260769 a(n) ~ sqrt(1 + sqrt(phi)) * 2^(n-1) * phi^(5*(2*n + 1)/4) / (5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. (End) %K A260769 nonn %O A260769 0,2 %A A260769 _N. J. A. Sloane_, Jul 30 2015 %E A260769 More terms from _Lars Blomberg_, Aug 01 2015