A130908 E.g.f.: exp(x+x^2/2!+x^3/3!)/(1-x).
1, 2, 6, 23, 106, 576, 3622, 26006, 210828, 1910096, 19162096, 211095732, 2534829376, 32962249568, 461527198056, 6923249156336, 110774157354832, 1883174989346016, 33897247428278368, 644048388555567536, 12880972761058252896, 270500465268345299072, 5951010522336442007776, 136873244273143429751328
Offset: 0
Keywords
Programs
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Mathematica
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 *) -
PARI
x='x+O('x^66); Vec(serlaplace(exp(x+x^2/2!+x^3/3!)/(1-x))) \\ Joerg Arndt, Jun 01 2014
Formula
a(n) ~ n! * exp(5/3). - Vaclav Kotesovec, Aug 04 2014
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
Extensions
Incorrect initial term 1 removed by Harvey P. Dale, Jun 01 2014