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 A052857 #36 Jan 13 2025 08:34:08
%S A052857 0,1,2,15,184,3145,68976,1846999,58413440,2130740721,88061420800,
%T A052857 4066862460991,207556068584448,11600364266112505,704664527894104064,
%U A052857 46226086991634882375,3256882066245640093696,245279323467051422886241
%N A052857 A simple grammar. a(n)=n*A052873(n-1).
%H A052857 G. C. Greubel, <a href="/A052857/b052857.txt">Table of n, a(n) for n = 0..250</a>
%H A052857 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=825">Encyclopedia of Combinatorial Structures 825</a>
%H A052857 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A052857 E.g.f.: exp(RootOf(exp(_Z)*x*_Z+exp(_Z)*x-_Z))*x.
%F A052857 a(n) = (n-1)!*Sum_{k=1..n-1} n^k*binomial(n-2,k-1)/k!, a(1)=1. - _Vladimir Kruchinin_, May 10 2011
%F A052857 a(n) = n!*hypergeom([-n+2], [2], -n) for n>=2. - _Peter Luschny_, Apr 20 2016
%F A052857 a(n) ~ exp(n/phi - n) * phi^(2*n-2) * n^(n-1) / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Oct 01 2017
%F A052857 E.g.f. A(x) satisfies: A(x) = x*exp(A(x)/(1 - A(x))). - _Ilya Gutkovskiy_, Apr 04 2019
%F A052857 a(n) = n * (n-2)! * LaguerreL(n-2, 1, -n) with a(0) = 0 and a(1) = 1. - _G. C. Greubel_, Feb 23 2021
%p A052857 spec := [S,{C=Set(B),S=Prod(Z,C),B=Sequence(S,1<= card)},labeled]:
%p A052857 seq(combstruct[count](spec,size=n), n=0..20);
%p A052857 # Alternatively:
%p A052857 a := n -> `if`(n<2,n, n!*hypergeom([-n+2],[2],-n));
%p A052857 seq(simplify(a(n)), n=0..17); # _Peter Luschny_, Apr 20 2016
%t A052857 Table[If[0<=n<=1, n, (n-1)! Sum[(n^k Binomial[n-2, k-1])/k!, {k,n-1}]], {n,0,20}] (* _Michael De Vlieger_, Apr 20 2016 *)
%t A052857 Table[If[n<2, n, n*(n-2)!*LaguerreL[n-2, 1, -n]], {n, 0, 20}] (* _G. C. Greubel_, Feb 23 2021 *)
%o A052857 (Maxima)
%o A052857 a(n):=if n=1 then 1 else ((n-1)!*sum((n^k*binomial(n-2,k-1))/k!,k,1,n-1)); /* _Vladimir Kruchinin_, May 10 2011 */
%o A052857 (SageMath) [n if n<2 else n*factorial(n-2)*gen_laguerre(n-2, 1, -n) for n in (0..20)] # _G. C. Greubel_, Feb 23 2021
%o A052857 (Magma) [n lt 2 select n else n*Factorial(n-2)*Evaluate(LaguerrePolynomial(n-2, 1), -n): n in [0..20]]; // _G. C. Greubel_, Feb 23 2021
%K A052857 easy,nonn
%O A052857 0,3
%A A052857 encyclopedia(AT)pommard.inria.fr, Jan 25 2000