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 A082545 #39 Aug 15 2022 04:20:57
%S A082545 1,3,21,229,3393,63591,1442173,38398641,1174226049,40558249963,
%T A082545 1561734494661,66335687785533,3081211226192641,155369391396527439,
%U A082545 8452596370942940973,493494408990278911561,30777323181433121541633,2042075395611656190239571
%N A082545 a(n) = (2*n)! * Sum_{k=0..n} binomial(n,k)/(n+k)!.
%H A082545 Seiichi Manyama, <a href="/A082545/b082545.txt">Table of n, a(n) for n = 0..365</a>
%F A082545 a(n) = n!*LaguerreL(n, n, -1).
%F A082545 n*a(n) + (n^3-5*n^2-n+2)*a(n-1) - 2*(n+1)*(2*n-3)*(n-1)^2*a(n-2) = 0. - _Vladeta Jovovic_, Jul 16 2004
%F A082545 E.g.f.: exp((-2*x+1-(1-4*x)^(1/2))/(2*x))/(1-4*x)^(1/2). - _Mark van Hoeij_, Oct 31 2011
%F A082545 a(n) ~ n^n*2^(2*n+1/2)/exp(n-1). - _Vaclav Kotesovec_, Sep 27 2012
%F A082545 a(n) = n!*binomial(2*n,n)*hypergeom([-n], [1+n], -1). - _Peter Luschny_, May 04 2017
%F A082545 a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+1). - _Ilya Gutkovskiy_, Nov 21 2017
%p A082545 a:= n-> simplify(n!*LaguerreL(n$2, -1)):
%p A082545 seq(a(n), n=0..20); # _Alois P. Heinz_, Jul 27 2017
%t A082545 Table[n!*LaguerreL[n, n, -1], {n,0,17}] (* _Jean-François Alcover_, Jun 04 2019 *)
%o A082545 (PARI) a(n) = sum(k=0, n, k!*binomial(n, k)*binomial(2*n, k)); \\ _Seiichi Manyama_, May 01 2021
%o A082545 (PARI) a(n) = n!*pollaguerre(n, n, -1); \\ _Seiichi Manyama_, May 01 2021
%o A082545 (Magma) [Factorial(n)*Evaluate(LaguerrePolynomial(n, n), -1): n in [0..40]]; // _G. C. Greubel_, Aug 11 2022
%o A082545 (SageMath) [factorial(n)*gen_laguerre(n, n, -1) for n in (0..40)] # _G. C. Greubel_, Aug 11 2022
%Y A082545 Cf. A006902, A343832.
%K A082545 nonn
%O A082545 0,2
%A A082545 _Vladeta Jovovic_, May 11 2003