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A293117 E.g.f.: exp(x^2/(x-1)).

%I A293117 #18 Apr 30 2021 06:30:38
%S A293117 1,0,-2,-6,-12,0,240,2520,21840,181440,1481760,11642400,80498880,
%T A293117 311351040,-4739454720,-183437654400,-4300276780800,-88851284121600,
%U A293117 -1754954007206400,-34107089784768000,-659574028252339200,-12724865943229440000,-244046146272658329600
%N A293117 E.g.f.: exp(x^2/(x-1)).
%H A293117 Seiichi Manyama, <a href="/A293117/b293117.txt">Table of n, a(n) for n = 0..450</a>
%F A293117 D-finite with recurrence a(n) = (2*n-2)*a(n-1) - (n^2-n)*a(n-2) + (n^2-3*n+2)*a(n-3). - _Robert Israel_, Apr 29 2021
%p A293117 a:= proc(n) option remember; `if`(n=0, 1, -add(
%p A293117       a(n-j)*binomial(n-1, j-1)*j!, j=2..n))
%p A293117     end:
%p A293117 seq(a(n), n=0..25);  # _Alois P. Heinz_, Sep 30 2017
%t A293117 CoefficientList[Series[E^(-x^2/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2017 *)
%o A293117 (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^2/(x-1))))
%Y A293117 Column k=1 of A293119.
%Y A293117 Cf. A052845.
%K A293117 sign
%O A293117 0,3
%A A293117 _Seiichi Manyama_, Sep 30 2017