OFFSET
0,2
COMMENTS
From Vladimir Joseph Stephan Orlovsky, Jul 09 2011: (Start)
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-43,104,-155,146,-85,28,-4).
FORMULA
G.f.: 1 / (((1-2*x)^2)*(1-x)^6).
a(n) = A055249(n+7, 7).
For n >= 1, a(n) = A035039(n+7) + Sum_{j=0..n-1} a(j).
a(n) = Sum_{k=0..n+6} Sum_{i=0..n+6} (i-k) * C(n-k+6,i+4). - Wesley Ivan Hurt, Sep 19 2017
a(n) = (1/120)*(38520 - 75*2^(9+n) + 2*(9637 + 15*2^(8+n))*n + 4285*n^2 + 525*n^3 + 35*n^4 + n^5). - Colin Barker, Sep 20 2017
MAPLE
a:= n-> (Matrix(8, (i, j)-> if (i=j-1) then 1 elif j=1 then [10, -43, 104, -155, 146, -85, 28, -4][i] else 0 fi)^(n))[1, 1]: seq(a(n), n=0..25); # Alois P. Heinz, Aug 05 2008
MATHEMATICA
Table[Sum[(-1)^(n - k) k (-1)^(n - k) Binomial[n + 6, k + 6], {k, 0, n}], {n, 1, 26}] (* Zerinvary Lajos, Jul 08 2009 *)
PROG
(PARI) Vec(1 / ((1 - x)^6*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Sep 20 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wolfdieter Lang, May 26 2000
STATUS
approved