OFFSET
0,2
COMMENTS
Binomial transform of A081904.
3rd binomial transform of binomial(n+6, 6).
4th 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 (28, -336, 2240, -8960, 21504, -28672, 16384).
FORMULA
a(n) = 4^n*(n^6 + 129*n^5 + 5845*n^4 + 115215*n^3 + 993874*n^2 + 3308616*n + 2949120)/2949120.
G.f.: (1-3*x)^6/(1-4*x)^7.
a(n) = 28*a(n-1) - 336*a(n-2) + 2240*a(n-3) - 8960*a(n-4) + 21504*a(n-5) - 28672*a(n-6) + 16384*a(n-7); a(0)=1, a(1)=10, a(2)=79, a(3)=552, a(4)=3567, a(5)=21810, a(6)=127905. - Harvey P. Dale, Aug 14 2014
E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(4*x) / 720. - G. C. Greubel, Oct 17 2018
MATHEMATICA
CoefficientList[Series[(1-3x)^6/(1-4x)^7, {x, 0, 20}], x] (* or *) LinearRecurrence[{28, -336, 2240, -8960, 21504, -28672, 16384}, {1, 10, 79, 552, 3567, 21810, 127905}, 20] (* Harvey P. Dale, Aug 14 2014 *)
PROG
(PARI) x='x+O(x^30); Vec((1-3*x)^6/(1-4*x)^7) \\ G. C. Greubel, Oct 17 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^6/(1-4*x)^7)); // G. C. Greubel, Oct 17 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved