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 A302182 #17 Apr 20 2025 03:48:51
%S A302182 1,1,5,12,62,200,1065,3990,21714,89082,492366,2147376,12004740,
%T A302182 54718092,308559537,1454116950,8255788970,39935276810,227976044010,
%U A302182 1126178350440,6457854821340,32456552441040,186814834574550,952569927106980,5500292590186380,28391993275117500
%N A302182 Number of 3D walks of type abc.
%C A302182 See Dershowitz (2017) for precise definition.
%H A302182 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 A302182 From _Mélika Tebni_, Nov 27 2024: (Start)
%F A302182 a(n) = Sum_{k=0..n} binomial(n, k)*A126120(k)*A018224(n-k).
%F A302182 a(2*n+1) = A135394(n) / (2*n+2).
%F A302182 a(2*n) = A302181(n). (End)
%o A302182 (Python)
%o A302182 from math import comb as binomial
%o A302182 def row(n: int) -> list[int]:
%o A302182 return sum(binomial(n, k)*binomial(k, k//2)//(k//2+1)*((k+1) %2)*binomial(n-k, (n-k)//2)**2 for k in range(n+1))
%o A302182 for n in range(26): print(row(n)) # _Mélika Tebni_, Nov 27 2024
%Y A302182 Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.
%Y A302182 Cf. A018224, A126120, A135394, A302181.
%K A302182 nonn,walk
%O A302182 0,3
%A A302182 _N. J. A. Sloane_, Apr 09 2018
%E A302182 a(13)-a(25) from _Mélika Tebni_, Nov 27 2024