OFFSET
0,2
COMMENTS
If X is an n-set and Y a fixed 7-subset of X then a(n-7) is equal to the number of 7-subsets of X intersecting Y. - Milan Janjic, Jul 30 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 227.
Milan Janjic, Two Enumerative Functions
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: (1-x^7)/(1-x)^8 = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 )/(1-x)^7.
a(-1-n) = a(n).
720*a(n) = 720 + 1764*n + 2128*n^2 + 735*n^3 + 385*n^4 + 21*n^5 + 7*n^6. - R. J. Mathar, Mar 14 2011
MAPLE
seq(binomial(n+7, 7) - binomial(n, 7), n=0..30); # G. C. Greubel, Nov 09 2019
MATHEMATICA
Table[Binomial[n+7, 7] - Binomial[n, 7], {n, 0, 30}] (* G. C. Greubel, Nov 09 2019 *)
PROG
(PARI) a(n)=binomial(n+7, 7)-binomial(n, 7)
(Magma) [(720 + 1764*n +735*n^3 +2128*n^2 +385*n^4 +21*n^5 + 7*n^6)/720: n in [0..30]]; // Vincenzo Librandi, Oct 08 2011
(Sage) b=binomial; [b(n+7, 7) - b(n, 7) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) B:=Binomial;; List([0..30], n-> B(n+7, 7)-B(n, 7) ); # G. C. Greubel, Nov 09 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved