A003014 Expansion of e.g.f.: 1 + x*exp(x) + x^2*exp(2*x) + x^3*exp(3*x).

1, 1, 4, 21, 124, 705, 3726, 18361, 85240, 376641, 1597690, 6551721, 26116740, 101647585, 387634534, 1452554265, 5360857456, 19523426433, 70272302706, 250318462537, 883418329660, 3091835703201, 10739780397214

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (20,-175,878,-2779,5744,-7737,6534,-3132,648).

Formula

a(n) = n + n*(n-1)*2^(n-2) + n*(n-1)*(n-2)*3^(n-3). - Ralf Stephan, Mar 24 2004

Mathematica

With[{nn=30}, CoefficientList[Series[1+x Exp[x]+x^2 Exp[2x]+x^3 Exp[3x], {x, 0, nn}], x] Range[0, nn]!] (* or *) LinearRecurrence[{20, -175, 878, -2779, 5744, -7737, 6534, -3132, 648}, {1, 1, 4, 21, 124, 705, 3726, 18361, 85240, 376641}, 30] (* Harvey P. Dale, Mar 29 2016 *)

Prog

(Magma) [1], [(n+1) + n*(n+1)*2^(n-1) + n*(n+1)*(n-1)*3^(n-2) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011

Crossrefs

Sequence in context: A277292 A001888 A103769 * A108404 A115136 A364866

Adjacent sequences: A003011 A003012 A003013 * A003015 A003016 A003017

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Definition clarified by Harvey P. Dale, Mar 29 2016

Status

approved