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%I #22 Sep 08 2022 08:45:11
%S 0,1,3,10,39,176,905,5244,34111,250480,2108529,20751380,241315151,
%T 3282366504,50786289385,865850559196,15856276032255,306665879765984,
%U 6199863566817761,130237717066988580,2832527601333186319
%N Expansion of e.g.f.: (1-exp(x/(x-1)))/(1-x).
%H G. C. Greubel, <a href="/A087860/b087860.txt">Table of n, a(n) for n = 0..448</a>
%F a(n) = n!*(1 - LaguerreL(n, 1)).
%F a(n) = 3*(n-1)*a(n-1) - (n-1)*(3*n - 5)*a(n-2) + (n-2)^2*(n-1)*a(n-3). - _Vaclav Kotesovec_, Nov 13 2017
%F Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * (1 - BesselJ(0,2*sqrt(x))). - _Ilya Gutkovskiy_, Jul 17 2020
%F a(n) = n*n!*hypergeom([1 - n, 1], [2, 2], 1). - _Peter Luschny_, May 10 2021
%F a(n) ~ n! * (1 - exp(1/2)*cos(2*sqrt(n) - Pi/4) / (sqrt(Pi) * n^(1/4))). - _Vaclav Kotesovec_, May 10 2021
%t With[{nn=20},CoefficientList[Series[(1-Exp[x/(x-1)])/(1-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 27 2015 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace((1-exp(x/(x-1)))/(1-x)))) \\ _G. C. Greubel_, Feb 06 2018
%o (Magma) I:=[1,3,10]; [0] cat [n le 3 select I[n] else 3*(n-1)*Self(n-1) - (n-1)*(3*n-5)*Self(n-2) +(n-1)*(n-2)^2*Self(n-3): n in [1..30]];
%Y Cf. A009940, A070779.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Oct 25 2003
%E Definition clarified by _Harvey P. Dale_, Nov 27 2015
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