OFFSET
0,2
COMMENTS
Equals binomial transform of [1, 12, 54, 108, 81, 0, 0, 0, ...] where (1, 12, 54, 108, 81) = row 4 of triangle A013610. - Gary W. Adamson, Jul 19 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (8 + 6*n + 81*n^2 - 18*n^3 + 27*n^4)/8.
G.f.: (1+2*x)^4/(1-x)^5.
E.g.f.: (1/8)*(8 + 96*x + 216*x^2 + 144*x^3 + 27*x^4)*exp(x). - G. C. Greubel, May 26 2021
MAPLE
seq((8+6*n+81*n^2-18*n^3+27*n^4)/8, n=0..40); # G. C. Greubel, May 26 2021
MATHEMATICA
CoefficientList[Series[(1+2x)^4/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 13, 79, 307, 886}, 40] (* Harvey P. Dale, Sep 18 2024 *)
PROG
(Magma) [(8+6*n+81*n^2-18*n^3+27*n^4)/8: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(Sage) [(8+6*n+81*n^2-18*n^3+27*n^4)/8 for n in (0..40)] # G. C. Greubel, May 26 2021
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Paul Barry, Mar 23 2003
STATUS
approved