OFFSET
0,2
COMMENTS
Binomial transform of A081914. 4th binomial transform of (1,0,0,1,0,0,0,0,...). Case k=4 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f.: (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..150
Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256)
FORMULA
a(n) = 4^n*(n^3 - 3n^2 + 2n + 384)/384.
G.f.: (1 - 12x + 48x^2 - 63x^3)/(1-4x)^4.
MATHEMATICA
LinearRecurrence[{16, -96, 256, -256}, {1, 4, 16, 65}, 30] (* Harvey P. Dale, Aug 14 2017 *)
CoefficientList[Series[(1 - 12x + 48x^2 - 63x^3)/(1-4x)^4 , {x, 0, 30}], x] (* Stefano Spezia, Sep 02 2018 *)
PROG
(Magma) [4^n*(n^3-3*n^2+2*n+384)/384: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
(PARI) a(n)=4^n*(n^3-3*n^2+2*n+384)/384 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 31 2003
STATUS
approved