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%I #11 Mar 30 2012 18:55:29
%S 1,9,1046,519918,681617304,1853340127320,9049964145536880,
%T 72083636411763075120,874164613833481641471360,
%U 15325066482283901592487889280,372998446683217113984893861356800
%N Integral_{x=0..infinity} (x + x^2 + x^3)^n exp(-x).
%t Trinomial[n_, k_] := If[k == 0, 1, Coefficient[(1 + x + x^2)^n, x^k]]; a[n_] := Sum[Trinomial[n, k](n + k)!, {k, 0, 2n}]; Table[a[n], {n, 0, 20}]
%K nonn
%O 0,2
%A _Emanuele Munarini_, Jan 25 2011