OFFSET
0,1
COMMENTS
a(n) = ((n*...*(n+5))+(n+...+(n+5)))/3, n >= 0.
Binomial transform of 5, 242, 1200, 2400, 2400, 1200, 240, 0, 0, 0, 0, ....
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (n^6 + 15n^5 + 85n^4 + 225n^3 + 274n^2 + 126n + 15)/3. - Charles R Greathouse IV, Nov 04 2009
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6)+240 for n > 5; a(0)=5, a(1)=247, a(2)=1689, a(3)=6731, a(4)=20173, a(5)=50415. - Klaus Brockhaus, Nov 14 2009
G.f.: (5+212*x+65*x^2-80*x^3+55*x^4-20*x^5+3*x^6)/(1-x)^7. - Klaus Brockhaus, Nov 14 2009
EXAMPLE
a(0) = (0*1*2*3*4*5+0+1+2+3+4+5)/3 = (0+15)/3 = 5.
a(1) = (1*2*3*4*5*6+1+2+3+4+5+6)/3 = (720+21)/3 = 247.
MATHEMATICA
lst={}; Do[p=(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n+(n+5)+(n+4)+(n+3)+(n+2)+(n+1)+n; AppendTo[lst, p/3], {n, 0, 5!}]; lst
(Plus@@#+Times@@#)/3&/@Partition[Range[0, 30], 6, 1] (* Harvey P. Dale, Nov 10 2009 *)
PROG
(Magma) [ (&*s + &+s)/3 where s is [n..n+5]: n in [0..25] ]; // Klaus Brockhaus, Nov 14 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Oct 24 2009
EXTENSIONS
Edited and offset corrected by Klaus Brockhaus, Nov 14 2009
STATUS
approved