OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).
FORMULA
a(n)= A063265(n+2, 7)= (n+1)*(n+2)*(n+10)*(n^4 + 22*n^3 + 193*n^2 + 792*n + 1512)/7!.
G.f.: (2-x)*(1-x+x^2)*(3-3*x+x^2)/(1-x)^8; the numerator polynomial is N7(7, x) = 6 - 15*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5 from row n=7 of array A063266.
a(n) = binomial(n+7,n) - binomial(n+1,n). - Zerinvary Lajos, Jun 23 2006
a(n) = binomial(n+7,n) + binomial(n+6,n) + binomial(n+5,n) + binomial(n+4,n) + binomial(n+3,n) + binomial(n+2,n). - Zerinvary Lajos, Jun 23 2006
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=6, a(1)=33, a(2)=116, a(3)=325, a(4)=786, a(5)=1709, a(6)=3424, a(7)=6426. - Harvey P. Dale, Jan 06 2012
MAPLE
[seq((binomial(n+7, n)-binomial(n+1, n)), n=1..29)]; # Zerinvary Lajos, Jun 23 2006
MATHEMATICA
Table[Binomial[n+7, n]-Binomial[n+1, n], {n, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {6, 33, 116, 325, 786, 1709, 3424, 6426}, 30] (* Harvey P. Dale, Jan 06 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 24 2001
EXTENSIONS
More terms from Zerinvary Lajos, Jun 23 2006
STATUS
approved