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A003014 Expansion of e.g.f.: 1 + x*exp(x) + x^2*exp(2*x) + x^3*exp(3*x). 1
1, 1, 4, 21, 124, 705, 3726, 18361, 85240, 376641, 1597690, 6551721, 26116740, 101647585, 387634534, 1452554265, 5360857456, 19523426433, 70272302706, 250318462537, 883418329660, 3091835703201, 10739780397214 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition clarified by Harvey P. Dale, Mar 29 2016
STATUS
approved

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Last modified June 24 16:27 EDT 2024. Contains 373679 sequences. (Running on oeis4.)