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 A302179 #34 Jan 06 2025 16:18:05
%S A302179 1,1,4,9,40,120,570,1995,9898,38178,195216,805266,4209084,18239364,
%T A302179 96941130,436235085,2349133930,10891439130,59272544760,281544587610,
%U A302179 1545550116240,7489973640240,41416083787260,204122127237210,1135679731004700,5678398655023500,31760915181412800,160789633105902300
%N A302179 The number of 3D walks of length n in an octant returning to axis of origin.
%H A302179 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. The sequence is type aac in Table 3.
%H A302179 Mélika Tebni, <a href="http://retoz.free.fr/decembre2024.pdf">Fonctions de Bessel et cheminements en 3D</a>, Dec 2024.
%F A302179 a(n) = Sum_{i=0..n, j=0..n-i, i,j even} A126120(i) * A126120(j) * A001405(n-i-j) * n!/(i! * j! * (n-i-j)!). - _Nachum Dershowitz_, Aug 06 2020
%F A302179 E.g.f.: (BesselI(1, 2*x)/x)^2*(BesselI(0, 2*x) + BesselI(1, 2*x)). - _Mélika Tebni_, Jan 06 2025
%o A302179 (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
%o A302179 f(n) = binomial(n, floor(n/2)); \\ A001405
%o A302179 a(n) = sum(i=0, n, if (!(i%2), sum(j=0, n-i, if (!(j%2), C(i/2)*C(j/2)*f(n-i-j)*n!/(i! * j! * (n-i-j)!))))); \\ _Michel Marcus_, Aug 07 2020
%Y A302179 Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.
%K A302179 nonn,walk
%O A302179 0,3
%A A302179 _N. J. A. Sloane_, Apr 09 2018
%E A302179 a(13)-a(27) from _Nachum Dershowitz_, Aug 04 2020