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A194019 E.g.f. = exp(-x*(x+4)/2)/(1-x)^3. 0

%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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Last modified March 29 08:01 EDT 2024. Contains 371265 sequences. (Running on oeis4.)