OFFSET
0,2
COMMENTS
Binomial transform of A081902.
4th binomial transform of binomial(n+5, 5).
5th 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 (30,-375,2500,-9375,18750,-15625).
FORMULA
a(n) = 5^n*(n^5 + 115*n^4 + 4285*n^3 + 61325*n^2 + 309274*n + 375000)/375000.
G.f.: (1 - 4*x)^5/(1 - 5*x)^6.
E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(5*x)/120. - G. C. Greubel, Oct 18 2018
MATHEMATICA
LinearRecurrence[{30, -375, 2500, -9375, 18750, -15625}, {1, 10, 85, 660, 4830, 33876}, 30] (* Harvey P. Dale, Sep 27 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1-4*x)^5/(1-5*x)^6) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^5/(1-5*x)^6); // G. C. Greubel, Oct 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved