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E.g.f.: exp(x+x^2/2!+x^3/3!)/(1-x).
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%I #16 Jan 23 2024 20:26:21

%S 1,2,6,23,106,576,3622,26006,210828,1910096,19162096,211095732,

%T 2534829376,32962249568,461527198056,6923249156336,110774157354832,

%U 1883174989346016,33897247428278368,644048388555567536,12880972761058252896,270500465268345299072,5951010522336442007776,136873244273143429751328

%N E.g.f.: exp(x+x^2/2!+x^3/3!)/(1-x).

%F a(n) ~ n! * exp(5/3). - _Vaclav Kotesovec_, Aug 04 2014

%F D-finite with recurrence +2*a(n) +2*(-n-1)*a(n-1) +(n-1)*(n-2)*a(n-3) +(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 20 2021

%t With[{nn=20},CoefficientList[Series[Exp[x+x^2/2!+x^3/3!]/(1-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 01 2014 *)

%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x+x^2/2!+x^3/3!)/(1-x))) \\ _Joerg Arndt_, Jun 01 2014

%Y Cf. A130905, A130906, A130907.

%K nonn

%O 0,2

%A _Karol A. Penson_, Jun 08 2007

%E Incorrect initial term 1 removed by _Harvey P. Dale_, Jun 01 2014