OFFSET
0,2
COMMENTS
Binomial transform of A081905.
4th binomial transform of binomial(n+6, 6).
5th binomial transform of (1,6,15,20,15,6,1,0,0,0,...).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (35,-525,4375,-21875,65625,-109375, 78125).
FORMULA
a(n) = 5^n*(n^6 + 165*n^5 + 9535*n^4 + 238575*n^3 + 2590024*n^2 + 10661700*n + 11250000)/11250000.
G.f.: (1-4*x)^6/(1-5*x)^7.
E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(5*x) / 720. - G. C. Greubel, Oct 17 2018
MATHEMATICA
LinearRecurrence[{35, -525, 4375, -21875, 65625, -109375, 78125}, {1, 11, 100, 820, 6290, 46006, 324556}, 50] (* G. C. Greubel, Oct 17 2018 *)
PROG
(PARI) x='x+O(x^30); Vec((1-4*x)^6/(1-5*x)^7) \\ G. C. Greubel, Oct 17 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^6/(1-5*x)^7)); // G. C. Greubel, Oct 17 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved