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 A097662 #22 Aug 17 2022 22:31:17
%S A097662 0,1,6,33,208,1545,13326,130921,1441728,17572113,234662230,3405357681,
%T A097662 53334454416,896324308633,16083557845278,306827170866105,
%U A097662 6199668952527616,132240988644215841,2968971263911288998,69974827707903049153,1727194482044146637520,44552237162692939114281
%N A097662 a(n) = A002720(n) - 1.
%H A097662 G. C. Greubel, <a href="/A097662/b097662.txt">Table of n, a(n) for n = 0..440</a>
%F A097662 a(n) = Sum_{k=1..n} (n!^2 / k!*(n-k)!^2).
%F A097662 a(n) = Sum_{k=1..n} P(n, k)*C(n, k) where P(n,k), are the permutation coefficients A008279.
%F A097662 a(n) = n * A129833(n-1) for n>=1. - _Peter Luschny_, Oct 11 2016
%F A097662 From _G. C. Greubel_, Aug 11 2022: (Start)
%F A097662 E.g.f.: exp(x/(1-x))/(1-x) - exp(x).
%F A097662 Sum_{n >= 0} a(n)*x^n/(n!)^2 = (exp(x) -1)*BesselI(0, 2*sqrt(x)). (End)
%p A097662 a := n -> hypergeom([-n, -n], [], 1) - 1:
%p A097662 seq(simplify(a(n)), n=0..26); # _Peter Luschny_, Oct 11 2016
%t A097662 Table[n!*LaguerreL[n,-1] -1, {n,0,40}] (* _G. C. Greubel_, Aug 11 2022 *)
%o A097662 (Magma) [Factorial(n)*Evaluate(LaguerrePolynomial(n), -1) -1: n in [0..40]]; // _G. C. Greubel_, Aug 11 2022
%o A097662 (SageMath) [factorial(n)*laguerre(n, -1) -1 for n in (0..40)] # _G. C. Greubel_, Aug 11 2022
%Y A097662 Cf. A002720, A008279, A129833.
%Y A097662 Main diagonal of A329655.
%K A097662 nonn
%O A097662 0,3
%A A097662 _Ross La Haye_, Sep 20 2004