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 A377704 #24 Nov 26 2024 08:42:00
%S A377704 1,1,3,15,330,50388,225792840,202355008436035,
%T A377704 1051518440185020535448910,6295006026005594769305465540976338825800,
%U A377704 250690498666352364302787619036257555981545221373940020366174361300,76323919118339641225070197870691336391548146418602896138838604379490915124967820851616650659494440178513500
%N A377704 a(n) = binomial(Fibonacci(n)+Fibonacci(n+1)-2,Fibonacci(n)-1).
%C A377704 Number of staircase walks in a Fibonacci(n) X Fibonacci(n+1) grid where Fibonacci is A000045.
%H A377704 Paolo Xausa, <a href="/A377704/b377704.txt">Table of n, a(n) for n = 1..16</a>
%H A377704 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StaircaseWalk.html">Staircase Walk</a>
%F A377704 a(n) = binomial(Fibonacci(n)+Fibonacci(n+1)-2,Fibonacci(n)-1).
%F A377704 a(n) = binomial(Fibonacci(n+2)-2,Fibonacci(n)-1).
%F A377704 a(n) >= Sum_{k=1..n-1} a(k) for n > 1.
%F A377704 a(n) = binomial(Fibonacci(n+2)-2,Fibonacci(n+1)-1). - _Chai Wah Wu_, Nov 22 2024
%t A377704 Table[Binomial[Fibonacci[n+2] - 2, Fibonacci[n] - 1], {n, 12}] (* _Paolo Xausa_, Nov 24 2024 *)
%o A377704 (Python)
%o A377704 from sympy import binomial, fibonacci
%o A377704 a = lambda n: binomial(fibonacci(n+2)-2,fibonacci(n)-1)
%o A377704 print([a(n) for n in range(1, 13)])
%o A377704 (Python)
%o A377704 from math import comb
%o A377704 from gmpy2 import fib2
%o A377704 def A377704(n): return comb(*(lambda x:(x[0]-2,x[1]-1))(fib2(n+2))) # _Chai Wah Wu_, Nov 22 2024
%Y A377704 Cf. A000045, A000984 (staircase walks in a nXn grid), A001700 (staircase walks in a nX(n+1) grid).
%K A377704 nonn
%O A377704 1,3
%A A377704 _Darío Clavijo_, Nov 04 2024