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%I #14 Jan 26 2014 15:37:03
%S 2,5,16,59,254,1297,7820,54791,438394,3945629,39456392,434020435,
%T 5208245366,67707189929,947900659204,14218509888287,227496158212850,
%U 3867434689618741,69613824413137664,1322662663849615979,26453253276992319982,555518318816838720065
%N E.g.f. exp(x)*(x^2+x+2)/(1-x).
%H Vincenzo Librandi, <a href="/A107283/b107283.txt">Table of n, a(n) for n = 0..200</a>
%F Recurrence: (4*n+3)*a(n) = (4*n^2 + 7*n + 20)*a(n-1) - (4*n^2 + 16*n - 11)*a(n-2) + 9*(n-2)*a(n-3). - _Vaclav Kotesovec_, Oct 17 2012
%F a(n) ~ 4*e*n!. - _Vaclav Kotesovec_, Oct 17 2012
%t CoefficientList[Series[E^x*(x^2+x+2)/(1-x), {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x)*(x^2+x+2)/(1-x))) \\ _Joerg Arndt_, May 15 2013
%Y Cf. A030297.
%K easy,nonn
%O 0,1
%A _Creighton Dement_, May 19 2005
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