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%I #14 Sep 28 2023 04:24:25
%S 1,1,4,42,888,31920,1750320,136115280,14254007040,1934091250560,
%T 330078373228800,69199130042380800,17481751115946163200,
%U 5237838647954514201600,1836425205487182172262400,744852154338379227748608000,346052141662324885396697088000,182572078442025253754006986752000
%N a(n) = n!*A001515(n-1) with a(0) = 1.
%H N. J. A. Sloane, <a href="/A143990/b143990.txt">Table of n, a(n) for n = 0..101</a>
%F a(n) = n*(2*n-3)*a(n-1) + n*(n-1)*a(n-2), a(0)=1, a(1)=1. - _Sergei N. Gladkovskii_, May 17 2013
%F From _G. C. Greubel_, Sep 27 2023: (Start)
%F a(n) = n * A105749(n-1) + [n=0].
%F a(n) = n! * A144301(n).
%F E.g.f.: 1 + sqrt(Pi*x/2) * exp(-(1-x)^2/(2*x)) * erfi((1-x)/sqrt(2*x)).
%F Sum_{n >= 0} a(n)*x^n/(n!)^2 = exp(1 - sqrt(1-2*x)). (End)
%t With[{m=30}, CoefficientList[Series[Exp[1-Sqrt[1-2*x]], {x,0,m}], x]*(Range[0, m]!)^2] (* _G. C. Greubel_, Sep 27 2023 *)
%o (Magma) [n le 2 select 1 else (n-1)*(2*n-5)*Self(n-1) + (n-1)*(n-2)*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Sep 27 2023
%o (SageMath)
%o m=30
%o P.<x> = PowerSeriesRing(QQ, m+2)
%o def A143990(n): return (factorial(n))^2*P( exp(1-sqrt(1-2*x)) ).list()[n]
%o [A143990(n) for n in range(m+1)] # _G. C. Greubel_, Sep 27 2023
%Y Cf. A001515, A105749, A144301.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Dec 02 2008
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