%I #11 Aug 20 2021 06:31:54
%S 1,1,3,13,67,423,3133,26479,251529,2651041,30680659,386635269,
%T 5268724987,77182895047,1209369057453,20180004340087,357229013263057,
%U 6686021868702081,131910248042613091,2735955184504781629,59512017882001393011,1354597373468317860391,32199995769317030466013,797895597172079337217983
%N E.g.f. = exp(-x*(x+4)/2)/(1-x)^3.
%C E.g.f. satisfies (1-x)*f'(x) = (1+x+x^2)*f(x).
%F a(n) ~ n!*exp(-5/2)*n^2/2. - _Vaclav Kotesovec_, Jun 27 2013
%F D-finite with recurrence a(n) -n*a(n-1) +(-n+1)*a(n-2) -(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Aug 20 2021
%p read transforms; Order:=25; ics:=f(0)=1;
%p e1:=(1-x)*diff(f(x),x) = (1+x+x^2)*f(x);
%p dsolve({e1,ics},f(x),series);
%p SERIESTOLISTMULT(rhs(%));
%t CoefficientList[Series[E^(-x*(x+4)/2)/(1-x)^3, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Aug 12 2011
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