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 A052712 #32 Apr 15 2023 10:08:27
%S A052712 0,1,2,24,480,13440,483840,21288960,1107025920,66421555200,
%T A052712 4516665753600,343266597273600,28834394170982400,2652764263730380800,
%U A052712 265276426373038080000,28649854048288112640000
%N A052712 Expansion of e.g.f. (1 + 4*x - sqrt(1-8*x))/8.
%C A052712 Also the number of random walk labelings of the 2 X (n-1) king's graph, for n > 1. - _Sela Fried_, Apr 14 2023
%H A052712 G. C. Greubel, <a href="/A052712/b052712.txt">Table of n, a(n) for n = 0..330</a>
%H A052712 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=668">Encyclopedia of Combinatorial Structures 668</a>
%H A052712 Sela Fried and Toufik Mansour, <a href="https://arxiv.org/abs/2304.05728">Graph labelings obtainable by random walks</a>, arXiv:2304.05728 [math.CO], 2023.
%F A052712 D-finite with recurrence: a(0) = 0, a(1)=1, a(2)=2, a(n+1) = 4*(2*n-1)*a(n).
%F A052712 a(n) = 8^(n+1)*Gamma(n+3/2)/sqrt(Pi).
%F A052712 a(n) = n!*A003645(n-2), n>1. - _R. J. Mathar_, Oct 18 2013
%F A052712 G.f.: (1 + 4*x - 2F0([1,-1/2], [], 8*x))/8. - _R. J. Mathar_, Jan 25 2020
%p A052712 spec := [S,{B=Prod(C,C),C=Union(B,S),S=Union(B,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052712 Table[n!*2^(n-2)*CatalanNumber[n-1] +Boole[n==1]/2 +Boole[n==0]/4, {n,0,30}] (* _G. C. Greubel_, May 30 2022 *)
%o A052712 (SageMath) [2^(n-2)*factorial(n)*catalan_number(n-1) +bool(n==0)/8 +bool(n==1)/2 for n in (0..30)] # _G. C. Greubel_, May 30 2022
%Y A052712 Cf. A052711, A052713, A052714, A052715, A052716, A052717, A052718, A052719, A052720, A052721, A052722, A052723.
%Y A052712 Cf. A000108, A003645.
%K A052712 easy,nonn
%O A052712 0,3
%A A052712 encyclopedia(AT)pommard.inria.fr, Jan 25 2000