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 A302184 #23 Apr 20 2025 04:08:41
%S A302184 1,2,7,26,108,472,2159,10194,49396,244328,1229308,6273896,32410096,
%T A302184 169181664,891181607,4731912082,25302648644,136150941064,736747902236,
%U A302184 4007011320808,21893702201648,120125750018656,661630546993116,3656966382542984,20278320788680912,112782556853239712
%N A302184 Number of 3D walks of type abe.
%C A302184 See Dershowitz (2017) for precise definition.
%H A302184 Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard's Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
%F A302184 a(n) = Sum_{k=0..n} binomial(n, k)*A126120(k)*A000984(n-k). - _Mélika Tebni_, Nov 30 2024
%p A302184 a := n -> 2*add(binomial(n, k)*binomial(k, k/2)*binomial(2*(n-k), n-k)/(k+2), k = 0..n, 2): seq(a(n), n = 0..25); # _Peter Luschny_, Nov 30 2024
%o A302184 (Python)
%o A302184 from math import comb as binomial
%o A302184 def a(n: int):
%o A302184 return sum(binomial(n, k)*binomial(k, k//2)//(k//2+1)*((k+1) %2)*binomial(2*(n-k), n-k) for k in range(n+1))
%o A302184 print([a(n) for n in range(26)]) # _Mélika Tebni_, Nov 30 2024
%Y A302184 Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A126120, A138547, A145847, A145867, A150500, A202814.
%K A302184 nonn,walk
%O A302184 0,2
%A A302184 _N. J. A. Sloane_, Apr 09 2018
%E A302184 a(12)-a(25) from _Mélika Tebni_, Nov 30 2024