OFFSET
0,2
COMMENTS
Binomial transform of A055852.
2nd binomial transform of binomial(n+5, 5).
3rd binomial transform of (1,5,10,10,5,1,0,0,0,...).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729).
FORMULA
a(n) = 3^n*(n^5 + 65*n^4 + 1385*n^3 + 11575*n^2 + 35574*n + 29160)/29160.
G.f.: (1 - 2*x)^5/(1 - 3*x)^6.
E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(3*x)/120. - G. C. Greubel, Oct 18 2018
MATHEMATICA
LinearRecurrence[{18, -135, 540, -1215, 1458, -729}, {1, 8, 49, 262, 1286, 5944}, 50] (* G. C. Greubel, Oct 18 2018 *)
CoefficientList[Series[(1-2x)^5/(1-3x)^6, {x, 0, 30}], x] (* Harvey P. Dale, Oct 22 2024 *)
PROG
(PARI) x='x+O('x^30); Vec((1-2*x)^5/(1-3*x)^6) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^5/(1-3*x)^6)); // G. C. Greubel, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved