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%I #18 Mar 01 2023 14:39:36
%S 1,0,2,-6,36,-240,1920,-17640,183120,-2116800,26943840,-374220000,
%T 5628934080,-91122071040,1579034096640,-29155689763200,
%U 571308920582400,-11838533804697600,258608278645516800,-5938673374272038400,143003892952893772800
%N Expansion of e.g.f. exp(x^2/(1+x)).
%H Seiichi Manyama, <a href="/A293120/b293120.txt">Table of n, a(n) for n = 0..444</a>
%F E.g.f.: exp(x^2/(1+x)).
%F a(n) = (-1)^n * A052845(n).
%F a(n) ~ (-1)^n * n^(n-1/4) * exp(-3/2 + 2*sqrt(n) - n)/sqrt(2). - _Vaclav Kotesovec_, Sep 30 2017
%t CoefficientList[Series[E^(x^2/(1+x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2017 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^2/(1+x))))
%Y Column k=1 of A293133.
%Y Cf. A111884, A293121.
%Y Cf. A052845.
%K sign
%O 0,3
%A _Seiichi Manyama_, Sep 30 2017
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